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FLUORESCENCE AND 
PHOSPHORESCENCE 



by PETER PRINGSHEIM 

Argonne National Laboratory, Chicago, Illinois 




19 4 9 



INTERSCIENCE PUBLISHERS, INC., NEW YORK 

INTERSCIENCE PUBLISHERS LTD., LONDON 



tf 4-S S 3V7i 



All Rights Reserved 

This book or any part thereof must not be repro- 
duced without permission of the publisher in 
writing. This applies specifically to photostatic 
and microfilm reproductions. 

Reprinted by Photo Offset 1961 



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HARRIS G0LIE61 
PRESTON 



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INTERSCIENCE PUBLISHERS, INC. 

215 Fo urth Ave., New York 3, N.Y. 
.For Great Britain and Northern Ireland: 



INTERSCrEKCE PUBLISHERS LTD. 

2a Southampton Row, London, W.C. 1 



To my Friend JAMES FRANCK 

A Pioneer in the Field 
of Fluorescence 



PREFACE 

The manuscript of this book was forwarded to the publishers on 
New Year's Day 1946, which proved to be most unfortunate timing. 
Within a few weeks from this date the investigations that had been 
kept secret or had been published in books and journals inaccessible 
during the war began to flow freely in ever-increasing numbers. They 
partly corroborated my earlier judgments and partly corrected them, 
or provided completely new facts and viewpoints. It must have been 
as trying for the patience of the publishers as it was exciting and even 
tantalizing for the author, when one section after the other, especially 
in the second part of the book, had to be revised or even rewritten. 

The manuscript that was finished in December, 1945, was already 
based on an earlier one whose intended publication in England had 
been prevented by the outbreak of the war. This genesis and stepwise 
growth may be recognizable in the present form of the book but, as 
I hope, not entirely to its disadvantage. It is probable that, if one were 
to start today to compile the material for a treatise on fluorescence 
and phosphorescence, one would be tempted to put much more 
emphasis on the latest developments, especially in the field of crystal 
phosphors, and to neglect not only the chapters dealing with the 
luminescence of gases and vapois but also the earlier work on the 
crystal phosphors themselves. It is curious to see how inclined one is 
to assume that research did not begin much before 1936; and the 
programs of three major congresses show in a very striking way to 
what extent the general interest has been shifted since 1936 from one 
end of the field to the other. In the reports of the first international 
luminescence congress held in Warsaw in 1936, papers on the fluo- 
rescence of vapors and gases still take more than fifty per cent of the 
space, and most of the other papers treated the luminescence of organic 
compounds. In the luminescence discussion of the Faraday Society at 
Oxford in 1938, the luminescence of solids takes about three times 
more space than the luminescence of liquids and vapors combined; 
and in the volume in which the papers presented at the meeting in 
Ithaca in October, 1946, are collected (it bears the title Luminescence 
of Solids), gases and vapors do not occur at all and the so-called 
organophosphors are mentioned in a single discussion remark. 



Viii PREFACE 

This trend is due, of course, to the growing importance crystal 
phosphors have attained in numerous technical applications, whereas 
on the other hand the fluorescence of gases, which contributed so much 
to the earlier development of the theory of atomic and molecular 
spectra, has become almost a closed chapter of classical optics. The 
intention in writing this book has been to give, for the first time in 
more than twenty years, a complete survey of the field of photo- 
luminescence. All types of practical applications have been left aside, 
since recent publications dealing with the various fields of this kind 
are available in sufficient numbers. Notwithstanding the fact that 
its title might suggest a more general content, the subject of the book 
has been restricted to photoluminescence. Luminescence excited by 
other means has not been included, although the luminescence excited 
by electrically charged particles at least is highly interesting and 
important. The main reason for this exclusion was the desire not to 
make the book too voluminous. But it cannot be denied that the 
principal importance of electroluminescence lies in its manifold tech- 
nical applications and that the investigation of these phenomena up 
to now has contributed far less to the theoretical understanding of 
the processes occurring in luminescence than has the study of photo- 
luminescence. 

As pointed out above, I tried during the period in which the book 
was edited and printed to take care as far as possible of newly pub- 
lished papers and also of the earlier publications that had previously 
escaped my attention. This was possible, of course, only within 
certain limits. Although Solid Luminescent Materials, edited by Fonda 
and Seitz, appeared in 1948, I was able to make use of some of the 
papers contained in the volume because I had been present at the 
meeting at Ithaca. On the other hand, Kroeger's exceedingly interest- 
ing volume, Some Aspects of the Luminescence of Solids, came too late 
and only insofar as its content had been published previously in 
various journals could some of his numerous new data be inserted. 

However, as may be seen from the great number of references 
with a, b, c, etc. in the bibliography, the latter lists every paper about 
photoluminescence of which I became aware up to May, 1948, again 
disregarding all papers dealing exclusively with technical applications. 
It is probable that, although containing well over two thousand 
items, the bibliography is not free of omissions, even for the years 
preceding the war, for the list of references that I kept continuously 
from 1908 on was not at my disposal and I had to start the collection 
all over again. 



PREFACE IX 

I have already mentioned that the publishers — the president 
and vice president of Interscience Publishers, Inc., as well as their 
whole staff — were exceedingly patient and helpful in the production 
of the book, and I want once more to thank them for their kindness. 
I want moreover to thank those of my colleagues who assisted me in 
various ways: my old friend J. Franck, with whom I discussed many 
a problem; S. Simon, who kindly corrected the galleys; F. Urbach, 
who not only read the page proofs but also suggested several impor- 
tant improvements, especially in the chapter on crystal phosphors 
for which he is one of the best authorities; Miss M. M. Tippet, who 
helped in correlating the bibliography; J. Biegeleisen, who was the 
first to draw my attention to the recently declassified report on the 
uranyl spectra and thus made it possible to bring this very important 
chapter up to date; and many others who helped me by putting at 
my disposal original photographs and sending me reprints of their 
papers. 



Chicago, December 1Q48 Peter Pringsheim 



CONTENTS 

Preface vn 

Introduction 1 

A. General Theory 1 

1. Postulates of Bohr's Quantum Theory 1 

2. Energy Levels 2 

3. Duration of the Luminescence Process 3 

4. Effects of Perturbations 5 

5. Coherence of the Secondary Radiation 7 

6. Comparison with Other Excitation Processes 9 

B. Experimental Technique 10 

7. Phosphoroscopes and Fluorometers 10 

8. Measurement of the Intensity and of the Degree of Polarization 17 

9. Light Filters and Light Sources 19 

10. Containers 23 

PART I. FLUORESCENCE OF GASES AND VAPORS 

I. Monatomic Cases and Vapors 27 

A. Nomenclature of Series Spectra 27 

11. Quantum Numbers 27 

12. Energy Terms 28 

13. Series Lines 30 

B. Fluorescence Lines 32 

14. Resonance Lines 32 

15. Multiple Ground States 34 

16. Excitation by Absorption of Lines Leading to Higher Energy 
States 36 

17. Stepwise Excitation 38 

18. Combined Electrical and Optical Excitation 44 

C. The absorption and Emission Process 48 

19. Absorption of Primary Radiation 48 

20. Fluorescence Yield and Width of Resonance Lines 51 

21. Hyperfine Structure 54 

22. Experimental Determination of Lifetime t 58 

23. "Imprisoned Radiation." Recoil of Excited Atoms 61 

D. Polarization of Resonance Radiation in Magnetic Fields 63 

24. Classical and Quantum-Mechanical Interpretation 63 

25. The Mercury Line 2537A as Most Simple Example 64 

26. Anomalous Zeeman Effects 68 

27. Negative and Circular Polarization 70 

xi 



Xll CONTENTS 

28. Vanishing Magnetic Fields 74 

29. Influence of Hyperfine Structure on Polarization of the Re- 
sonance Radiation 75 

E. Determination of t from the Degree of Polarization in Weak Magnetic 
Fields 79 

30. Principle of the Method 79 

31. Experimental Results 81 

32. Alternating Magnetic Fields 85 

F. Stark Effect in Resonance Radiation 86 

33. Direct Demonstration of the Effect 86 

34. Polarization of Resonance Radiation in Electric Fields ... 88 

G. Perturbations of Resonance Radiation by Collisions 89 

35. Effective Cross Sections 89 

36. Collision-broadening. Flame Fluorescence 92 

37. Transfer of the Excited Atom into Adjacent Quantum States . 96 

38. Effect of Collisions on the Polarization of Resonance Radiation 102 

39. Quenching of Resonance Radiation by Collisions 108 

40. Mechanism of Energy Transfer in Quenching Collision .... 116 
H. Sensitized Fluorescence 124 

41. Nature of the Phenomenon and Importance of Energy Re- 
sonance 124 

42. Influence of Foreign Gases and of Magnetic Fields 131 

II. Diatomic Gases and Vapors 134 

A. Theory of Band Spectra and Interpretation of Resonance Spectra . 134 

43. Energy Levels 134 

44. Rotational Doublets and the Complete Resonance Spectrum . 138 

45. Electronic Terms 142 

46. Shape of the Potential Curves 145 

47. Franck-Condon (F. C.) Principle 147 

B. Fluorescence of the Halogen Vapors 151 

48. The Visible Band System of I 2 151 

49. Ultraviolet Resonance Spectra of Iodine Vapor 161 

50. McLennan Bands 165 

51. Other Halogen Vapors 167 

C. Vapors of the Alkali Metals 169 

52. Existence of Diatomic Molecules 169 

53. Resonance Spectra of Na 2 170 

54. KNa, K 2 , Li 2 , Rb 2 , and Cs 2 175 

D. Elements of the Sixth Column of the Periodic System 177 

55. Oxygen 177 

56. Resonance Spectra of S a , Se 2 , and Te 2 177 

57. Predissociation and Fluctuations 181 

E. Fluorescence of Other Diatomic Molecules 184 

58. Elements of the Fifth Column of the Periodic System .... 184 

59. Various Metal Vapors 185 

60. Light and Heavy Hydrogen 186 



CONTENTS Xlll 

61. Metal Halide Vapors 187 

62. Fluorescence of Diatomic Radicals 189 

F. Effect of Collisions and of Magnetic Fields on the Resonance Spectra 

of Diatomic Molecules 191 

63. Various Effects Produced by Collisions 191 

64. "Transferring Collisions" in Iodine Vapor 192 

65. Quenching of Iodine Fluorescence by Foreign Gases 196 

66. Quenching of Iodine Fluorescence by Magnetic Fields .... 199 

67. Transferring Collisions and Induced Predissociation in Other 
Diatomic Molecules 201 

68. Atomic Fluorescence Caused by Induced Predissociation . . 207 

G. Photodissociation of Diatomic Molecules Followed by Atomic Fluor- 
escence 208 

69. Products of Photodissociation 208 

70. Dissociation of Metal Halides and Their Heat of Dissociation . 208 

H. Lifetime of the Excited States and Polarization of the Resonance 

Spectra 212 

71. Lifetime 212 

72. Theory of the Polarization of Resonance Spectra 213 

73. Experimental Results 215 

I. Sensitized Fluorescence of Diatomic Molecules 218 

74. Fluorescence Bands Excited in Hg- and Cd-Vapors on Addition 

of Foreign Gases 218 

75. Rare Gas-Mercury Bands 222 

J. Luminescence of Diatomic Metal Molecules That Are Stable Only in 

Excited States 224 

76. Fluorescence Bands of Hg 2 224 

77. Some Properties of the Individual Hg 2 -Bands 227 

78. Lifetime of the Bands and Their Sensitivity to Collisions . . 230 

79. Sensitized Fluorescence Induced by Hg 2 -Molecules 234 

80. Fluorescence Bands of Cd 2 , Zn 2 , and of Mixtures of Various 
Metal Vapors 235 

K. Re-emission of Exciting Lines and Rayleigh Scattering 238 

81. Re-emission of Exciting Lines by Molecules 238 

82. Rayleigh Scattering 240 

HI. Polyatomic Gases and Vapors 244 

A. Types of Fluorescence Spectra and the Energy Relations 244 

83. Some Distinguishing Properties of Polyatomic Molecules . . 244 

84. Stokes' Law and the Selection Rules 247 

B. Fluorescence Spectra of Polyatomic Molecules 250 

85. Inorganic Compounds 250 

86. Introductory Remarks Concerning the Fluorescence of Organic 
compounds 253 

87. Nonaromatic Organic Compounds 254 

88. Benzene 261 

89. Simple Derivatives of Benzene 266 

90. Condensed Aromatic Hydrocarbons 270 



X1 V CONTENTS 

91. Heterocyclic Compounds; Dyes 273 

92. Sensitized Fluorescence of Aromatic Compounds 274 

C. Fluorescence of Radicals Produced by Photodissociation of Poly- 
atomic Molecules 275 

93. Metal Halides 275 

94. Other Polyatomic Molecules 279 

PART II. FLUORESCENCE AND PHOSPHORESCENCE 
OF CONDENSED SYSTEMS 

TV. General Surrey 285 

A. Nature of Luminescent Substances 285 

95. Conditions for the Occurrence of Photoluminescence 285 

96. Most Important Types of Luminescent Substances 286 

97. Energy Transfer from the Absorbing to the Emitting Mechanism 287 

B. Course of the Emission Process 290 

98. Fluorescence and Phosphorescence 290 

99. Decay Curves 293 

100. Luminescence Intensity and "Light Sum" L . . 297 

C. Emission, Absorption, and Excitation Spectra 299 

101. Band Width, Stokes' Law, and the Franck-Condon Principle . 299 

102. So-called Mirror Symmetry 302 

103. Fluorescence Intensity as a Function of Absorbed Energy . . 306 

104. Absorption by Molecules in the Excited State 311 

D. Luminescence Yield as a Function of Experimental Conditions . . 313 

105. Definition of Yield and Methods of Measuring It 313 

106. Efficiency, Lifetime, and Solvent Quenching 315 

107. Quenching of Luminescence by Foreign Molecules of Low Con- 
centration 322 

108. Specific Properties of Quenchers 328 

109. Mechanism of Quenching by Foreign Molecules 335 

110. Fluorescent Compounds as Photosensitizers 338 

111. Fluorescence of Living Plants 343 

112. The "Optimum Concentration" 346 

113. Self-quenching 349 

114. Polymerization and Self-quenching 353 

115. Polymers with New Fluorescence Bands 359 

E. Fluorescence and Ionization 361 

116. Fluorescence of Neutral and Ionized Molecules 361 

117. Fluorescence and Photoelectric Effect 364 

F. Polarization and Angular Intensity Distribution of Fluorescence 
Radiation 366 

118. Polarization Caused by the Anisotropy of Oscillators .... 366 

119. Polarization of Fluorescence in Liquid Solutions and Influence 

of Molecular Rotation 370 

120. Negatively Polarized Fluorescence of Isotropic Solutions . . . 379 

121. Polarized Fluorescence of Partially Oriented Molecules . . . 383 



CONTENTS XV 

122. Polarized Fluorescence of Crystals 385 

123. Angular Intensity Distribution of the Fluorescent Radiation . 389 

V. Fluorescence of Organic Compounds 392 

A. The Luminescent Systems 392 

124. Chromophors and Fluorogens 392 

125. Influence of Isomerism 395 

126. Influence of State of Aggregation 397 

127. Influence of Solvent 400 

B. Aromatic Hydrocarbons and Heterocyclic Compounds 402 

128. Benzene 402 

129. Derivatives of Benzene 404 

130. Condensed Aromatic Hydrocarbons 405 

131. Heterocyclic Ring Compounds 415 

C. Dyes 420 

132. Synthetic Dyes 420 

133. Natural Dyes 424 

D. Polyenes. Aliphatic Compounds 429 

134. Aromatic and Aliphatic Polyenes 429 

135. Various Aliphatic Compounds 432 

E. Afterglow of Organic Compounds in Solid Solutions 434 

136. Phosphorescence and Slow Fluorescence 434 

137. Spectra of Dyes in Solid Solutions 445 

138. "Progressive Phosphorescence" and Related Phenomena . . 448 

139. Boric Acid and Similar Compounds as Bases of "Organo- 
phosphors" 453 

VI. Luminescence of Pure Inorganic Compounds 458 

A. The Rare-Earth Metals . .' 458 

140. Fluorescence Spectra of the Trivalent Ions 458 

141. The Crystalline State 465 

142. Solutions in Liquids and Glasses 474 

143. Fluorescence of Divalent Ions 478 

B. Uranyl Salts 480 

144. Band Spectra of UO^-Ions 480 

145. Fluorescence Spectra of Individual Crystalline Uranyl Salts . 489 

146. Liquid Solutions and Glasses 494 

C. Various Complex Inorganic Ions 498 

147. Metal Salts in Aqueous Solutions r-'»i*r"4?* 

148. "Pure" Inorganic Salts ./-■.-^Wf^Ot 

149. Complex Platinous Salts %.".,■;'•, $02 



150. Unsaturated Silicon Compounds '.; . >. ». '} $05 

SO: 



151. Glasses > : .\'lt 505 



VII. Crystal Phosphors '. W £ j|o8 

A. Nature of the Phosphors and Fundamental Processes 508 

152. Monomolecular and Bimolecular Processes 508 

153. Crystalline Structure of the Phosphors 516 



XVI CONTENTS 

154. Activating and Quenching Impurities 521 

155. Absorption and Emission Bands 526 

156. Photoconductivity and the Zone Theory of Crystals 532 

157. Phosphorescence Centers and Electron Traps 543 

158. Processes of Excitation and Emission 556 

159. Periods of Induction and Decay 566 

160. Phosphorescence Yield 582 

B. Properties of the Most Important Synthetic Crystal Phosphors . . 594 

161. Alkaline Earth Sulfide Phosphors and Related Phosphors . . 594 

162. "Pure" Sulfide and Oxide Phosphors 605 

163. Silicate Phosphors 610 

164. Halide Phosphors 616 

165. Phosphors with Various Base Materials 628 

166. Tungstates and Molybdates 634 

167. Chromium as Activator 637 

C. Luminescence of Natural Minerals and of Crystals Discolored by 
Irradiation 646 

168. Minerals and Gems 646 

169. Radioluminescence and "Radiophotoluminescence" 655 

170. Fluorites 660 

Bibliography 671 

Author Index 761 

Reference Number Index 761 

Subject Index 773 



INTRODUCTION 
A. General Theory 

1. Postulates of Bohr's Quantum Theory. By absorption of light 
the energy of the absorbing system is increased. According to the laws 
of thermodynamics the inverse process, emission of energy in the 
form of radiation, must be possible. This inverse process must occur, if 
no other way of returning the system to its initial state of lower 
energy is available. Light emission excited by light absorption is called 
photoluminescence. For a long time photoluminescence was supposed 
to be an exceptional phenomenon characteristic of relatively few 
substances. The real problem is, however, to understand why so many 
substances are -not photoluminescent. 

Bohr's theory, first developed for interpretation of the spectra of 
the H atom and later adapted to more and more complicated systems, 
postulates that energy can be taken up by such a system only in 
certain definite steps; the system is stable only in discrete, more or less 
sharply defined energy levels. The lowest of these levels is the ground 
level or the ground state of the system. For all atoms and for many 
diatomic molecules the energy levels are perfectly known. For poly- 
atomic molecules and for still more complicated systems like crystals, 
knowledge of the energy levels is still far from complete. Even for 
these systems however, the assumption of the existence of such energy 
levels has proved itself very fertile in developing an understanding of 
all processes connected with light absorption and light emission. 

Only if the energy absorbed by a molecule is so large that one 
part of the system is completely separated from the remainder, as in 
a process of ionization or dissociation, can the separating particles 
take up undetermined amounts of kinetic energy, so that no discrete 
energy levels exist for the system as a whole . 

In quantum mechanics a system in a given state is characterized 
by a "wave function" tf> which is the product of the wave functions ^,- 
of all individual particles composing the system. These functions ^ 
determine the probability with which a particle is found at a point 
in space. 

Apart from the introduction of discrete energy levels, Bohr's 

1 



GENERAL THEORY 



theory postulated the following relation for a transition between two 
levels N and F with the energies E N and E F : 

vfn = l/h-(E F —E N ) (1) 

h being Planck's constant = 6.63- 10~ 27 erg sec and v FN the frequency 
of the radiation which is emitted-or absorbed by the transition. 

In general, the wave number v = 1/A is used instead of the fre- 
quency v, which has the dimension of sec -1 , v is measured in cm -1 and 
is related to the frequency by the equation v = v/c. Hence a "term" 
T, which is characterized by its wave number v, has the energy vhc, 
but for the sake of brevity energies are frequently expressed in cm -1 . 
On the other hand, it is customary to measure energies in electron 
volts (eV), one electron volt being the energy which an electron 
acquires under the acceleration produced by a potential difference of 
one volt. 

leV m 8.11 • 10 3 cm -1 «a 1.59- 10~ 12 ergs & 23 kcal/mole 

2. Energy Levels. In the diagram of Figure 1 several energy levels 
of an atom or a more complicated system are represented by horizontal 
lines. The vertical distance between two of these lines is proportional 

to the corresponding difference in 
energy ; the level N represents the 
ground state. By absorption of 
light of frequency vps the atom is 
raised to the level Fandifnoother 
energy levels exist between N and 
F, the atom can return to iVonly 
by re-emission of light of the same 
frequency v NF : theoretically this 
is the simplest case of photo- 
luminescence; it is called "reso- 
nance radiation." In the diagram 
of Figure 1 , however, several levels 
C,D ... are located between N and 
F. Under these conditions other 
transitions from F to C, D ... can 
occur, resulting in the emission of spectral lines of frequency v Fc; 
v FD . . . These frequencies are smaller than v NF . The law according to 
which the wavelength of fluorescence is always greater than, or in the 
limiting case equal to, the wavelength of the exciting light was first 
found empirically by Stokes {1585) ; the quantum theoretical expla- 



T - 




, 


. 


"It 




















1 1 


1 . 


\ 














1 1 










1 






i 1 


| 










■ 


" 


-=^H=^ 









F' 

F 
M 



I 



Fig. 1. Energy level diagram for 

the representation of fluorescence 

and phosphorescence. 

1 : resonance radiation. 

2: phosphorescence. 

3: fluorescence. 

4 and 5 : anti-Stokes fluorescence. 



DURATION OF LUMINESCENCE PROCESS 3 

nation was given by Einstein more than fifty years later (344). Small 
deviations from Stokes' law are possible if other energy levels N' or F' 
are located immediately above N or F respectively, so that the system 
can be raised by transfer of thermal energy either into N' before the 
exciting light is absorbed, or into F' during the lifetime of the system 
in the excited state F. Under these conditions the frequency of the 
exciting light v FN > is smaller than the frequency of the fluorescence 
v FN , or the frequency of the absorbed light v FN is smaller than the 
frequency of the fluorescence v F - N : anti-Stokes fluorescence. 

Such deviations from Stokes' law, by which additional energy is 
supplied by a body of low temperature to the radiation from a source 
of much higher temperature, of course in no way invalidates the second 
law of thermodynamics, as was suggested erroneously by Lenard 
(I284,i2g^b, 1726, 1762b, 1762c) . 

3. Duration of the Luminescence Process. In the classical Lorentz- 
Drude theofy the emission of monochromatic light by an atom or 
molecule originates from the oscillation of an electron which is bound 
to its position of equilibrium by a quasi-elastic force. The decrease in 
energy of the oscillating electric dipole which is caused by the emission 
of radiation, and the corresponding decrease in intensity of the radi- 
ation itself, follow an exponential law. The average duration of the 
emission, or the time after which the intensity has dropped from its 
initial value 7 to (1 /e)I , is : 

3 mc 

* = i^^with/ ( =/ , * (2) 

For visible light, with v e& 5- 10 14 sec _1 , t is of the order of 10 -8 sec. 
In the absence of all external perturbations the lifetime of an 
exlcited state is determined, according to quantum theory, by the total 
probability of all possible transitions to lower energy levels. These 
transition probabilities A FK can be calculated if the wave functions 4>' 
and >ji" of the combining levels E F and E K are known : 



jww 



* 

rdv 



The lifetime of a molecule in the excited state F is then : 



T ~ ZA FK (2a) 

K 

As in radioactive decay, the number of transitions per unit of time 
is at every instant proportional to the number of excited molecules and 



4 GENERAL THEORY 

thus the decay of the luminescence intensity again follows an ex- 
ponential law, exactly as in the older theory. 

The transition probabilities between various levels of one and the 
same molecule are of widely different magnitudes. While the Lorentz- 
Drude theory dealt only with electric dipole radiation, with a mean 
lifetime depending exclusively on the frequency of the oscillator, much 
weaker radiation of much longer duration can also be explained on the 
ground of classical electrodynamics by assuming electric quadrupoles 
or multipoles or magnetic dipoles or multipoles as sources of radiation. 
The emission by an electric quadrupole or a magnetic dipole lasts 
about 10 6 times longer than that of an electric dipole. In the quantum- 
mechanical models, however, an electric dipole can have a much 
smaller moment than the oscillating electron of the Lorentz theory and 
thus the decay of its radiation also can be much slower. Several 
experimental methods have been found which allow a discrimination 
between the radiation of electric and magnetic dipoles and multipoles 
(28oa,435,i4Qi, 1492,17610). 

Transitions which have a very small probability because they 
correspond to the radiation of an electric dipole of small moment or 
of an electric multipole or a magnetic pole are called "forbidden" and 
the corresponding spectral lines are "forbidden lines." If no "allowed 
transition" from an excited state M to any lower energy level'exists, 
the system, once brought into this state, must remain in it for a 
relatively long period. Such states are termed "metastable." If the 
system is absolutely unperturbed (as, for instance, in the highly rare- 
fied atmospheres of stellar nebulas) light emission nevertheless occurs, 
but with very small intensity and slow decay. On the other hand, the 
transition from the ground state to the state M is also forbidden and 
the corresponding absorption line, if at all observable, is very weak. 
However, M can be reached indirectly ; in the level scheme of Figure 1, 
this can occur by absorption of the line corresponding to the transition 
F<- iV,*-and by the subsequent transition F -» M. If M is separated 
by only a small amount of energy from F and if the excited system is 
in thermal equilibrium with the surrounding molecules a sufficient 
amount of energy can be provided to the system so that it can return 
to F. From there the emission of the lines corresponding to the tran- 
sitions F^N, F->C, etc., may again take place. A photoluminescence 

* The symbol for the higher level always precedes the symbol for the lower 
level; the direction of the transition is indicated by the arrow. This principle, 
which is generally used for the description of the spectra of diatomic molecules, 
is applied here similarly to the representation of atomic spectra. 



EFFECTS OF PERTURBATIONS 5 

process of this type, involving the passage through a metastable level, 
is called phosphorescence. 

In the older literature fluorescence and phosphorescence were 
distinguished only by the criterion of an observable afterglow : if the 
luminescence did not last longer than the irradiation, it was called 
fluorescence ; if it was visible for an appreciable length of time after 
the end of the excitation, it was called phosphorescence. Modern 
experimental technique however, permits the measurement of the 
finite duration of any emission process, even if it is as short as 10~ 9 
sec, and, on the other hand, the spontaneous transition probabilities, 
even in atomic processes, correspond to lifetimes which vary continu- 
ously from 10 -8 sec to several seconds. Therefore, it is no longer 
possible to define some arbitrary duration of the emission process as 
the boundary between fluorescence and phosphorescence. (For a more 
completedefinitionoffluorescenceandphosphorescence, see chapter IV.) 

While, according to the definition given above, fluorescence and 
phosphorescence are first-order processes and follow exponential laws 
of decay, anotherkindof luminescence isa typical bimolecular reaction. 
If an electron is completely separated from its molecule by photo- 
electric ionization and if its recombination with any other ion produces 
the emission of light, the process is of the second order and decays, 
therefore, according to a hyperbolical law. Luminescence caused by 
recombination is observed in electrical discharge through gases or 
metal vapors under especially favorable conditions. These cannot be 
achieved in the case of excitation by light absorption. However, a 
phenomenon of the same kind occurs in certain phosphorescent 
crystals; it will be called "recombination afterglow" in the following 
treatment. 

4. Effects of Perturbations. An excited system can be transferred 
to neighboring energy levels by outside perturbations, for instance by 
collisions or other interactions with surrounding molecules, and from 
these new levels transitions occur which produce emission lines not 
contained in the primary fluorescence spectrum. Furthermore, such 
perturbations may cause a momentary displacement of an energy level 
and if these displacements fluctuate with time and in space, broad and 
diffuse bands appear instead of sharp lines in the absorption and 
fluorescence spectra. This is true in particular for all condensed systems 
which are capable of luminescence (with the exception of certain 
crystals, especially at low temperatures). Under such conditions the 
peak of the emission band must be shifted with respect to the peak of 
the corresponding absorption band in the direction of greater 



6 GENERAL THEORY 

wavelengths. This consequence of Stokes' law will be dealt with in 
more detail in a later chapter. 

If the whole energy of excited molecules can be lost as the result 
of collisions or other perturbations, the mean life of all excited mole- 
cules is shortened and the fluorescence yield is decreased. 

The quantum yield of fluorescence is : 

= II A (3) 

where the fluorescence intensity I and the radiant energy A absorbed 
per unit time are measured by the number of light quanta contained 
in the emitted and absorbed radiation. In the case of resonance 
radiation, the quantum yield Q can be replaced by the "energy 
yield" <5 (/ and A being given in ergs or calories), since in this case 
Q = (compare Section 105). [In general (namely in the case of 
Stokes fluorescence), the energy yield is smaller than the quantum 
yield, while in the case of anti-Stokes fluorescence is slightly larger 

than <?.] 

If no perturbations occur, the fluorescence intensity I is equal to 
A when equilibrium is reached during the irradiation, and Q = \. 
Under these conditions, the spontaneous transition probability a,, 
alone determines the lifetime t , and the number w of excited molecules 
in equilibrium is given by the equation : 

A — I = a n = « /t with r = l/ce and n = A/a (4) 

If the excitation energy can be lost by a second competing process 
with a probability a v Equation (4) is replaced by : 
A 1 =n 1 {a + a,) = njr 1 where t x = l/(a + a x ) and n x = A 1 l{a + a x ) (5) 

n x is smaller than n . Supposing that the absorbing power of the 
molecules is not altered by the perturbations (A x = A = I ), the 
fluorescence intensity becomes : 

I 1 = a a n x = Mj/t,, = IJ{1 + ctjTo) (6) 

and the yield: 

0i = hl A = Vi/Vo = tj/to (7) 

The "quenching constant" a x is: a t = — — (7a) 

Qi 

In the same way the yield is reduced by another perturbation with 
the probability <x 2 to: 

<? 2 = r J r o where t 2 = l/(a + a 2 ) (7b) 

Hence the general relation : 

Q 1 :e,=T 1 :T 1 (8) 



COHERENCE OF THE SECONDARY RADIATION 7 

The fluorescence yield of a given system is directly proportional to the 
actual lifetime of the excited state (1221,1571). 

If several processes compete simultaneously with the radiating 
transition and if their probabilities are a lt a 2 . . . a„, the lifetime of the 
excited state becomes: 

(9) 



C"o + cii + a 2 4- '• • • a» 
and the intensity of the luminescence : 



/„ = 



1 + T o( a i + a 2 + • • • a») 1 + T^a, + a 3 + . . . a n ) 



h 

: 3 + . . . a„) 

(10) 



1 + r^jOn 

According to the classical theory, the width of a spectral line is 
proportional to the damping coefficient or inversely proportional to the 
mean life of the excited state. Qualitatively the same law holds in 
quantum theory. All perturbations by which the fluorescence is 
quenched increase the width of the corresponding emission line. The 
latter is determined, however, not only by the action of the pertur- 
bation on the excited state from which the emission process originates, 
but also by the action on the final state to which the system is 
transferred. 

5. Coherence of the Secondary Radiation. The only photolumi- 
nescence process for which the classical wave theory of light could 
account without the introduction of rather artificial hypotheses was 
the excitation of resonance radiation. Existence of this phenomenon 
had been predicted on theoretical grounds by Lord Rayleigh long 
before its discovery by R. W. Wood. Resonance radiation was under- 
stood as special case of light scattering in which the scattering 
resonators were exactly in tune with the frequency of the primary 
radiation. 

According to the original quantum theory only the average 
lifetime t of an excited state could be determined, while for the indi- 
vidual molecule the time elapsing between the absorption and the 
re-emission of light obeyed the laws of statistics. Hence it seemed 
impossible that a definite phase relation could exist between the 
wave trains of the primary and the secondary light. Resonance 
radiation was considered to be incoherent. On the other hand Rayleigh 
scattering, which was known to be coherent, was ascribed to forced 
vibrations of "virtual oscillators" within the molecules. There was no 



8 GENERAL THEORY 

connection between the two phenomena. It was even assumed, for a 
time, that for radiation in resonance with the characteristic frequency 
of the scattering oscillators both processes might occur simultaneously 
and that it might be possible to separate them experimentally (e.g., 
by observing a different decay period for either of them) (129) . 

In the quantum-mechanical treatment, however, the electro- 
magnetic field produced by the interaction of the primary radiation 
and the virtual oscillators of a molecule is exactly the same as that of 
the classical wave theory, and thus the steady transition from 
Rayleigh scattering to resonance radiation is restored. If various 
energy levels C, D . . . exist in the molecule between the ground state 
N and the level F to which the .molecule is raised by the absorption of 
the primary light, the resulting electromagnetic field surrounding 
the excited molecule is the same as if it contained a number of 
vibrating oscillators of frequency v FC , v FD ... in addition to the 
absorbing oscillator of frequency v FN . The "strength" of each 
oscillator is proportional to one of the transition probabilities F -> C, 
F -> D . . . F -> N. All phenomena related to the wave nature of the 
secondary radiation (coherence, interference, polarization) are to be 
derived from this model. However, the energy of the radiation is no 
longer spread continuously over the whole wave field and proportional 
everywhere to the square of the wave amplitude. The square of the 
amplitude determines only the probability for a photon of the corre- 
sponding frequency to be found at a given instant at a particular point. 
The absorption and emission of radiant energy occurs exactly as in 
Bohr's original theory, in quanta within practically infinitely short 
periods of time (18 13). 

Insofar as the problem of coherence is determined by the phase 
relation between primary and secondary radiation, only Rayleigh 
scattering and resonance radiation can be considered (1529). The 
existence of such coherence is not revealed by any experimental facts. 
Resonance radiation is observed exclusively in gases and vapors at 
low pressures. Under these conditions the coherence of the "classical" 
Rayleigh scattering with the primary radiation cannot be proved 
either, because of the random distribution of the molecules in a 
perfect gas. 

If the fluorescence spectrum of a monatomic gas contains lines 
of wavelengths different from that of the exciting light, a constant 
phase relation between the waves of the primary and the secondary 
radiation is out of the question. However, a constant phase relation 
might still exist between the secondary wave trains originating at 



OTHER EXCITATION PROCESSES 9 

different atoms ; this kind of coherence could again only be observed 
by the angular distribution of the fluorescence intensity if the fluo- 
rescing atoms were fixed in space in a regular lattice. 

Every kind of coherence between the radiation coming from 
different molecules must disappear in the fluorescence of molecules in 
which nuclear vibrations and rotations occur simultaneously with the 
electronic transition and independently in each individual molecule. 
The same is true if the molecules undergo external perturbations 
during their lifetime in the excited state. This is the case for the 
fluorescence of all liquids and solids. On the other hand, it has been 
proved by wide-angle interference experiments that the radiation 
emanating in different directions from an individual molecule of a 
liquid solution is coherent, exactly as the radiation emitted by a-dipole 
as a spherical wave is coherent in itself according to the classical wave 
theory (433,1489-1492,1817). 

6. Comparison with Other Excitation Processes. The radiation 
emitted by an atom or a molecule depends only on its state of excitation 
and on the probabilities of transitions from this state to those of lower 
energy. It does not depend on the mode of excitation by which the 
system has been brought into the excited state. In this sense there is 
no difference between fluorescence and any other kind of light 
emission by the same atoms or molecules caused by collisions with 
electrons, by chemical processes, or by thermal agitation. The charac- 
teristic properties of a spectral line or a band (for instance, the 
dependence on temperature and pressure or the sensitivity to magnetic 
and electric fields) must be the same in every case. 

A system emitting luminescence is not, however, in a state of 
thermal equilibrium; some of its molecules contain a much higher 
electronic energy than that corresponding to the actual temperature 
of the system and this is the essential feature of every luminescence 
process. It follows that the "excited" molecules can lose their excessive 
energy by collisions with other molecules : luminescence, for instance 
the photoluminescence of iodine vapor, can be suppressed or 
"quenched" by the addition of relatively small quantities of oxygen. 
If the same quantity of oxygen is added to iodine vapor heated in a 
quartz tube to a temperature of 1000° C at which it emits its charac- 
teristic bands as temperature radiation according to Kirchhoff's law, 
no appreciable change in the emission occurs, because now, in thermal 
equilibrium, the quenching collisions must be compensated by an 
equal number of exciting collisions (1284). 

Photoluminescence is distinguished furthermore by an almost 



10 EXPERIMENTAL TECHNIQUE 

complete control of the excitation process, since, among all atoms or 
molecules which are present, only those in a well-defined initial state 
are transferred into an equally defined excited state by the absorption 
of light of a given frequency. The complete spectrum of all atoms and 
molecules, modified within certain limits by the temperature, is 
emitted by a flame or an arc. By means of electron collisions in a gas at 
low pressure it is possible to exclude from the spectrum all lines which 
require an excitation energy surpassing the energy of the electrons 
under the applied voltage, but all levels lying below this energy are 
excited simultaneously. Besides, the accuracy of the method is not 
great enough to differentiate between the excitation of closely adjacent 
lines. On the other hand, the possibility of separately exciting neigh- 
boring energy states of a molecule by the absorption of monochro- 
matic light is limited only by the degree to which the primary light 
can be made monochromatic. Even the state of polarization which is 
characteristic for a certain transition can be determined by this 
method of excitation ; thus itbecomes possible toascertain the existence 
of the various Zeeman levels in very weak magnetic fields which are 
separated by such small intervals that they cannot be distinguished 
by other spectroscopic methods. 

The same is still true, although to a smaller degree, for condensed 
systems; there, also, a much finer differentiation is obtained in the 
excitation of individual emission processes by light absorption than 
by any other mode of excitation-. 

B. Experimental Technique 

7. Phosphoroscopes and Fluorometers. The experimental methods 
applied to the investigation of photoluminescence are, in general, very 
simple. The most important types of apparatus which have been 
especially designed for this purpose are the phosphoroscopes and 
fluorometers. These serve for measuring the duration of short or 
almost instantaneously decaying emission processes. All of these 
instruments are based on the principle of permitting the observation of 
the luminescence a short, and if desired, a variable time after the end 
of the excitation period. 

The first phosphoroscope was invented by E. Becquerel (A, 78); 
in a "Becquerel phosphoroscope" the luminescent substance is placed 
between two discs M and N (Figure 2), which are mounted on a 
common axis and have sector-shaped apertures A and D shifted with 



PHOSPHOROSCOPES AND FLUOROMETERS 



11 



respect to each other by an angle <p. The exciting light enters the 
phosphoroscope by the apertures in one of the discs and the lumi- 
nescence light reaches the eye of the observer through the apertures' 
in the other disc. The time interval between excitation and obser- 
vation and the duration of the excitation itself can be varied within 
certain limits by altering the speed of rotation of the discs, the angle 
of aperture & of the sectors (which in the original apparatus was 
identical in the two discs), and the angle <p separating the sectors A 
from the sectors D. It is plausible that with decreasing "lifetime" the 




Fig. 2. Becquerel phosphoroscope. 



speed of rotation must be increased or the angle <p decreased in order 
to observe the afterglow. For quantitative observations the intensity 
of the luminescence must be measured by means of a photometer. 
For a correct interpretation of these observations, however, it is not 
sufficient to plot the measured intensities 7 as a function of the 
average time elapsed between excitation and observation, for instance 
as a function of the speed of rotation of the discs. The formula derived 
by Becquerel under this assumption was : 

3\— r, 



2« (log I j— log /,) 



11a 



T x and T 2 are the durations of a revolution of the discs at two different 
frequencies, I 1 and 7 2 the corresponding intensities of luminescence, and 
n the number of sectors in one of the discs. Equation (11) yields values 
of t which in some cases are more than twice as large as the true values. 
The equation does not take into account the fact (1) that the apertures 
A and D open and close only gradually, (2) that a luminescence with a 



12 EXPERIMENTAL TECHNIQUE 

finite decay period has also a finite period of growth, and (3) that the 
emission of light observed during each passage of a sector D is caused 
not only by irradiation in the last preceding period of excitation but 
possibly by that in many previous periods. Delorme and Perrin have 
published a method which permits an exact determination of t from 
the data obtained with a Becquerel phosphoroscope ; it necessitates a 
rather inconvenient graphical approximation of a theoretical curve to 
the curve which has been obtained experimentally. However the 
different corrections are made very nearly negligible by the intro- 
duction of some modifications in the original instrument : each disc has 
only one aperture, the aperture D for the observation of the lumin- 
escence being a narrow slit and the aperture A for the excitation a 
much larger one ; the two apertures and the speed of rotation are kept 
constant during a whole set of observations and only the angle <p 
between A and D is varied {272). 

It will be discussed later that a luminescence process which has 
a certain decay period t has also a corresponding period of growth or 
"induction". In general this induction period will not have reached its 
end at the end of an illumination period t x in a phosphoroscope. If the 
luminescence decays exponentially and if a stationary state is attained 
after a certain number of revolutions, the peak intensity of lumines- 
cence reached at the end of each illumination period is : 

1 e -tjz 

^-h 1 _ e -,,r ( llb > 

In this equation /„ is the luminescence intensity obtained under 
continuous illumination, t = t x -\- t 2 is the time of one revolution of 
the phosphoroscope, t x the duration of each illumination period, and 
t 2 the corresponding dark period, t is the mean decay time of the 
luminescence. I m approaches I the more, the larger t x and the smaller 
t is compared with t. 

By means of a Becquerel phosphoroscope mean lifetimes as short 
as 10~ 4 sec can be determined. The instrument can be used, however, 
only if the luminescent substance is transparent to some degree for 
either the exciting or the secondary radiation. If this is not the case, 
the apparatus must be altered so that the phosphor is excited and 
observed from the same side. This can be accomplished by fastening the 
phosphor to a cylinder rotating within a coaxial tube; the exciting 
light is admitted through a slit on one side of the tube and the lumi- 
nescence observed through a slit on the opposite side. Lenard has 
devised an apparatus in which a fast-moving diaphragm periodically 



PHOSPHOROSCOPES AND FLUOROMETERS 13 

screens the phosphor from the observer and simultaneously actuates 
a spark discharge exciting the luminescence (X). In still another setup, 
a pinpoint image of the primary light source is thrown on the phosphor 
which uniformly covers a rotating disc ; if luminescence is persistent, 
the point is drawn out into a bright streak and the length of the 
luminescent streak in conjunction with the known speed of rotation 
provides a measure of the duration of the afterglow (187,1766,1884). 
The latter arrangement has the advantage that at low frequency of 
rotation slow decay periods of the order of 1 sec can be observed; this is 
not possible with phosphoroscopes of the Becquerel type. With high 
speed of rotation, on the other hand, it is claimed that periods of 
afterglow of less than 10~ 5 sec can be measured. The device by means 
of which the shortest decay periods are observed with a mechanical 
shutter seems to be the one proposed by Vavilov and Levshin: the 
fluorescence is excited by the light from a spark discharge and the 
luminous spot is drawn out into a long band by means of a fast- 
revolving mirror, the spark always being started in the same position 
of the mirror by a synchronizing apparatus. The limit of the resolving 
power of this phosphoroscope is claimed to be 10 -6 sec (1766). A 
resolving power of a microsecond is reached also if a cathode-ray 
oscillograph is used for analyzing the fluctuating potential of a 
photoelectric cell which is excited by the luminescence. The primary 
radiation impinging on the luminescent substance must be interrupted 
by a rotating disc shutter which is in phase with the alternating 
voltage applied to the second pair of electrodes in the oscillograph 
tube. In phosphoroscopes of this type the intensity curve of the 
exciting radiation is made as nearly rectangular as possible so that the 
irradiation is nearly constant through a time interval of the order of 
5 millisec. The period of the oscillograph and of the shutter is about 
ten times as long and thus the complete rise ("induction") and decay 
of the luminescence are visualized in a single curve, if the luminescence 
has decayed to zero at the end of every oscillograph period. Otherwise, 
the emission processes originating from previous excitation processes 
will overlap in the same way as with other phosphoroscopes (266,4.596, 

I335a,i432c,i433)- 

An oscillograph phosphoroscope described by Lord and Rees 
differs from the more usual type in that the exciting radiation has a 
sinusoidal intensity curve. The light source and the time base of the 
oscillograph are actuated by the same alternating voltage so that they 
are synchronized automatically. The intensities of the primary 
radiation and of the luminescence as functions of time are recorded by 



14 



EXPERIMENTAL TECHNIQUE 



means of the oscillograph and the phase shift between the minima of 
the two curves is measured (957a). 

For the measurement of the very shortest decay periods down 
to 10~ 9 sec so-called fluorometers are used. They are, in principle, 
nothing else than modifications of the Becquerel phosphoroscope with 
practically no inertia. For this purpose the mechanical shutters are 
replaced by an electric device. Such shutters are either Kerr cells 
operated by a high-frequency alternating voltage and placed between 
crossed Nicols or they are systems in which the impinging light beam is 
diffracted periodically by means of supersonic waves. In contradis- 
tinction to the Becquerel phosphoroscope the time interval between 




Fig. 3. Kerr-cell fluorometer [Szymanowski (1623)] 
L : light source. K and S : compensating 

K 1 and K t : Kerr cells. arrangement for the 
Z: mirror. measurement of elliptic 

N v N 2 , N 3 , and N i : polarization. 

Nicols. T: fluorescent substance. 



excitation and observation is not produced by a phase difference 
between the oeriods of the first and the second shutter, but by the 
variation of the distance between the luminescent substance and the 
two shutters, and thus by the time in which the light traverses this 
distance. If this time is equal to one-half the period of the shutters, no 
light is transmitted through the second shutter, unless the luminescence 
has a duration which is not infinitely short compared to the period of 
the shutters. 

The first fluorometers which yielded useful results were of the 
Kerr-cell type. A somewhat improved modification of the original 
apparatus designed by Ga viola is shown schematically in Figure 3. 
L is the light source, T the fluorescent substance arid K x and K 2 the 
two Kerr cells placed between the two pairs of crossed Nicols N lt N 2 , 
and N 3 , 2V 4 , respectively. Instead of measuring the intensities of the 
luminescence for variable distances K x -T-K 2 , the degree of elliptical 
polarization of the radiation transmitted through the second Kerr 



PHOSPHOROSCOPES AND FLUOROMETERS 



15 



cell is determined. The fluorescent substance T and a diffusely re- 
flecting surface R (not shown in the figure) are mounted on a movable 
carriage and in every position of the carriage T and R are interchanged. 
Thus two complete curves of the measured ellipticities can be plotted, 
one for the instantaneous reflection process and the other for the 
luminescence process (main curve and fluorescence curve in Figure 4) . 
The value of t is, in the first approximation, derived directly from the 
distance between the minima in the two curves. For accurate calcu- 
lations several corrections must be introduced ; the complete theory of 
the method has been discussed by Duschinsky. According to Szyma- 




0.04 



Fig. 4. Curves obtained with the Kerr-cell fluorometer 

[Szymanowski (1623)]. 

ah and a/: ellipticity of reflected and of fluorescent 

light as a function of path length. 
gthtor'- calculated according to Duschinsky 's theory. 
/ and g ex p : intensities derived from a* and a/, respectively. 
/: distance K r -T-K^ in Fig. 3. 

nowski it is possible to measure decay periods as low as 10~ 9 sec with 
an error of ± . 2 • 1 -9 . The theory assumes that the decay is exponential . 
In principle it should even be possible to verify the validity of this 
assumption by analyzing the shape of the curves of Figure 4 (328,460b, 
1622-162 5). 

In some instances the fluorescence radiation is partially plane 
polarized if it is excited by plane-polarized light ; this is always the 
case in Kerr-cell fluorometers. Under these conditions different values 
of t are obtained according to whether the Nicols N 2 and N 3 are 
crossed or parallel, both positions being admissible. A partial or even 
total depolarization of the fluorescence light is caused by the Brownian 
rotation of the luminescent molecules during their decay period 
Hence the measurements average different portions of the decaycurve 
with crossed or with parallel Nicols N 2 and N 3 . The genuine average 



16 EXPERIMENTAL TECHNIQUE 

is obtained if the planes of polarization of N 2 and N 3 form an angle of 
54.72°. The validity of this consideration has been checked experi- 
mentally (669, 6y 6, 7 71). 

In supersonic-cell fluorometers a single cell serves for both shutters : 
it is traversed by the exciting radiation and by the fluorescence 
light in two directions perpendicular to each other, as shown in 
Figure 5. The supersonic waves are produced by means of high- 
frequency oscillating voltages in a solid quartz block to which the 
electrodes are directly applied, or in a vessel filled with a liquid. In the 
latter case the oscillations are generated by means of a thin quartz 
plate which is in contact with the liquid. Either arrangement has its 
advantage. The liquid cells require very little energy and low voltage, 
while a peak voltage of several thousand volts is needed for the quartz 
Ph block. On the other hand, it is much 

l J VT\7T L -' more difficult to obtain exactly plane 

\i& parallel wave trains in a liquid than 

ji 5 T in a good crystal. At the moment 



I _---A hr" l "f"A""--'tar when the amplitude of the standing 



\s wave passes through zero, light beams 
j i 7 " <^> traversing the cell are not deflected; 
1 1 1 ! when the amplitude of the supersonic 



^ 



X/p wave reaches its maximum a large 



i . ' part of the light is diffracted into the 

spectra of the first order. With good 
Fig. 5. Supersonic fluorometer ,■ , , , , , , ,. , 

(Maerks) adjustment the modulation is almost 

Light source to the left complete. In the main these fluoro- 

7\: supersonic cell as shutter. meters are operated in the same 

P x and P 2 : totally reflecting ag tfae Kerr . ceU instrume nts, 

prisms, mounted on earn- J 

age movable in direction ,4. with the exception that the light 

T 2 : fluorescent solution, ex- intensities must be measured photo- 

surf n ace a fl e "^ refleCting metrically. Maercks uses for this 

PA: differential photometer cell. purpose a differential photoelectric 

• s i- s 3 : sllts - cell in which the intensities of the 

directly transmitted and of the diffracted light beams are compared, 

thus eliminating the influence of intensity fluctuations of the primary 

light source (168,780,970,1708). 

Kerr-cells filled with nitrobenzene do not transmit the violet and 
u.v. Besides, they are rapidly heated by the great energy input of 
about 100 watts so that the measurements must be interrupted after a 
short time. On the other hand, the exact theoretical treatment has 
not yet been worked out for the supersonic shutters, because the "time 



INTENSITY AND THE DEGREE OF POLARIZATION 17 

function" which determines the transmitted energy during a full 
oscillation period as a function of the time is not known. In the first 
approximation it has been supposed to be sinusoidal, but the deviations 
may be rather large. 

Both instruments have the property in common that with the 
shutter frequencies of 10 7 which are needed for the measurement of 
short decay times, the paths over which the fluorescent substance 
must be moved in order to obtain a complete curve, as in Figure 4, are 
of the order of five meters. Thus the whole arrangement is rather 
cumbersome. Kirchhoff has overcome this drawback by a device which 
is somewhat complicated and seems to reduce the accuracy of the 
measurements. 

8. Measurement of the Intensity and of the Degree of Polarization. 
Any photometer can be used for the measurement of the intensity of 
fluorescence. It is true that a number of photometers are advertised 
as fluorometers or fluorimeters (for better distinction the name 
"fluoro-photometer" would be preferable), but they have no features 
by which they differ from similar instruments constructed for other 
purposes. Visual photometers, photogfaphic methods, or photo- 
electric cells, both of the emission and the barrier-layer type, are in 
general use. For the measurement of weak intensities Geiger- Mueller 
counters or "photo-multipliers" can replace the photocells. A visual 
photometer for the very 6mall intensities which occur frequently in 
the investigation of fluorescence has been designed by Vavilov. In this 
apparatus the fluorescence radiation and the comparison light are 
weakened by means of a neutral wedge to the threshold value of the 
dark adapted eye (183). 

As in all photometric work, it is of the greatest importance that 
any variations in the intensity of the primary light source are auto- 
matically compensated for and, therefore, it is advisable to use as 
comparison light the radiation of a fluorescent substance which is 
excited by the same primary source. The human eye and all photo- 
electric cells and photographic plates are characterized by a more or 
less selective response to light of different wavelengths. Therefore they 
cannot be used for comparing radiation of different color or different 
wavelength if the spectral distribution of their sensitivity is not 
known. The fact that the fluorescence yield of many fluorescent 
compounds is independent of the wavelength of the exciting light over 
a wide spectral range can be used for heterochromatic photometry. 
E. J. Bowen recommends as "integrating screens" mosaics made of 
uranyl sulfate or of cells filled with an esculin solution. Radiation, 



18 



EXPERIMENTAL TECHNIQUE 



the intensity of which is to be determined, excites the fluorescence of an 
integrating screen which covers the entrance window of a photoelectric 
cell and thus stimulates a current in the cell proportional to the 
unknown intensity (Figure 6) {140). 

Photoelectric cells are particularly suitable if the total amount of 
light which is stored in a phosphor after the end of the excitation is to 
be determined. This "light sum" is proportional to the electric charge 



L 






Fig. 6. Heterochromatic photometer (Bowen) . 
F v .F 2 , F 3 , D v and D 2 : light T x and T 2 : integrating 

filters . 
P,and P 2 : photoelectric cells. 



fluorescent screens. 
FL: fluorescent solution. 



produced in the photoelectric cell, which is connected to an electro- 
meter and a capacitance of known capacity. A light counter operating 
a mechanical counting device (telephone counter) is even more useful 
for the same purpose. Complete decay curves covering long periods 
of time are obtained with a photo-multiplier tube connected through 
an amplifier with a recording galvanometer. The curve can be followed 
over a very wide range of intensities, if the amplification can be altered 
by known steps every time the galvanometer deflection has reached 
a certain low value (733,837(1,1293). 

The degree of polarization of fluorescence radiation is frequently 
of great importance. For partially plane-polarized light the degree of 
polarization is defined by the 'equation: 

*= ( rTF) (12a) 

I' and I" are the maximum and the minimum intensities of the 
fluorescence if it is observed through a Nicol which is gradually rotated 
around its axis. The azimuths of maximum and minimum intensity 
are often known a priori, otherwise the preferential orientation of the 
electric vector has to be determined in order to obtain the real degree 
of polarization. The relation between the degree of polarization p and 
the degree of depolarization : 



LIGHT FILTERS AND LIGHT SCOURCES 19 

Q = /'//' (12b) 

is determined by the equations: 

Q = (1— P)f(i +P): P = (l— <?)/(! + (?) (12c) 

Sometimes the "apparent" degree of polarization p, is obtained 
experimentally instead of p : 

(I s —I x ) 

p ° = (T^y < 12d > 

where I z and I x are the intensities of the components with electric 
vectors parallel to two directions Z and X which are perpendicular to 
each other (as a rule, the vertical and the horizontal), p, can be zero 
even if p is equal to 100 % if the radiation is plane polarized parallel to 
a direction forming an angle of 45° with Z and X. In the following the 
term "light polarized parallel to a direction" is always used in the 
sense that the electric vector of the radiation is parallel to this 
direction; "light partially polarized parallel to a direction" means 
that the electric vector has its greatest amplitude in this direction. 

In general,, one of the following methods is used for the determi- 
nation of the degree of polarization. Either a double image of the 
luminescent light source is produced by means of a Wollaston prism 
and an analyzing Nicol adjusted to the angle at which the brightnesses 
of the two images become equal; or the partial polarization of the 
radiation is made visible by the interference fringes produced in a 
quartz-wedge combination (Savart plate, etc.) and the fringes are 
made to disappear by means of a compensating set of glass plates ; or 
the radiation enters a photoelectric cell through a polarizing prism and 
its intensity is measured for various azimuthal orientations of the 
prism. The quartz- wedge method is particularly suitable for visual 
measurements; the "Cornu method", or double-image method with 
photographic registration, and the photoelectric method, serve mainly 
for the u.v. (466). 

9. Light Filters and Light Sources. Colored screens, monochromators 
and spectrographs of usual types serve for the spectral resolution of 
the exciting radiation as well as of the luminescence light. Colored 
glasses of many shades are provided by several manufacturers 
(Corning, Schott, and others) and gelatin niters stained with organic 
dyes are also available (Kodak, Wratten). By a combination of such 
screens almost any spectral region can be isolated, though, in general, 
with great loss of luminosity. "Black" glass, stained with nickel 
oxide, is almost completely opaque for all visible light except the 



20 EXPERIMENTAL TECHNIQUE 

extreme red,* while its absorption coefficient is small between 4000 
and 3000A. The transparency reaches its maximum value of about 
80% at 3500A. Special glasses of this kind are even transparent as far 
as 2300A, -but they are not quite so opaque for the violet part of the 
spectrum. 

Some other filters which have proved useful for isolating spectral 
regions in the u.v. may be mentioned. A solution of 1.75 molar nickel 
sulfate and 0.5 molar cobalt sulfate in distilled water contained in a 
quartz cuvette of 3 cm thickness, absorbs all light of wavelengths 
greater than 3500A, but transmits 73 % of 3130A, 80 % of 2600A, and 
almost as much of 2300A. Similarly a quartz cell filled with bromine 
vapor completely cuts off all light from the yellow down to 3500A and 
chlorine vapor at saturation pressure at room temperature is opaque 
between 4400 and 2650A; both freely transmit the Hg-line 253 7A. 
On the other hand, the short wavelength radiation is absorbed by an 
aqueous solution of potassium nitrate from 4000A downward, by a 
solution of potassium phthalate from 3000A downward, and by a 
thiophene solution from 2500A downward. The Hg-lines 3132A and 
2537A, respectively, are still well transmitted by the two latter 
solutions. The Hg-line 1849A, which is transmitted through good 
crystalline quartz and moderate distances of atmospheric air, is 
completely absorbed by distilled water, while the Hg-line 1940A is 
transmitted. Adding acetic acid dropwise to distilled water shifts the 
limit of transparency continuously from 1940 to 2400A. 

Occasionally closely adjacent components of almost monochro- 
matic radiation are to be separated without the use of a spectrograph 
and the corresponding loss of intensity. R. W. Wood has devised the 
following setup for the separation of the sodium D-lines (Figure 7). 
The radiation containing both D lines {AX = 6A), which has been 
polarized by means of a first Nicol P v is passed through a crystalline 
quartz plate Q. The optical axis of the crystal lies in the plane of the 
plate and forms an angle of 45° with the electric vector of the incident 
radiation. The thickness of the plate, about 32 mm, is determined 
so that after leaving the plate the ordinary and the extraordinary rays 

* In order to eliminate this long wavelength radiation, which is often 
disturbing for visual observation, a cell containing a copper sulfate solution is 
frequently inserted in the path of the exciting light. However, it should not be 
overlooked that if this filter is sufficiently concentrated to eliminate the red 
completely, the near ultraviolet is also appreciably weakened. If the lumi- 
nescence is not red itself, it is therefore better to insert the filter in the path of 
the secondary radiation. For the absorption of infrared radiation a cell filled 
with distilled water suffices to protect the luminescent substance against heat. 



LIGHT FILTERS AND LIGHT SCOURCES 21 

have a phase difference which is larger by |A for D 2 than it is for D^ 
A second Nicol P 2 of suitable orientation transmits only one of the two 
lines (470,1879). 

For the partial isolation of components of the hyperfine structure 
of the Hg-line 2537A, which have an even closer spacing (AX ~ 10~~ 2 A), 
Mrozowski uses a polarizing prism and an absorption cell filled with 
mercury vapor which is placed in a magnetic field. If the strength of 
the magnetic field has a certain value, the absorption lines of the 
hyperfine structure are shifted so much that they absorb some of the 
components of the incident radiation while transmitting some of the 
others (io6y). 

Frequently, and especially if the exciting light is strongly 
scattered by the luminescent substance, it is advantageous to use the 



*-=a=tn£t^tsO 



Fig. 7. Wood's method for the separation 
of the D-lines. 
L: light source. P lt P 2 : Nicols. 
Q: quartz plate, if : resonance lamp. 

method of "crossed" or complementary filters. The first filter trans- 
mits only those parts of the primary radiation which serve for the 
excitation of the luminescence ; the second filter is placed between the 
luminescent substance and the eye of the observer and transmits the 
luminescence light, while it is opaque for the exciting radiation. (For 
instance, in Figure 6, the filters D 1 and £> 2 are complementary to the 
filter combination F lt F 2 F 3 .) This device, which has already been 
used by Stokes can, of course, be applied only if the spectral region of 
the exciting light does not completely overlap that of the emission 
band. If this condition is fulfilled, it becomes possible to observe the 
fluorescence, during the excitation, in the direction of the primary 
radiation, a procedure which is often convenient, and, in certain cases, 
of especial interest. If the first filter is a "black glass" transmitting 
only u.v., the second filter can be dispensed with (594). 

More detailed information concerning the specific action of 
exciting light of different wavelengths (the so-called "excitation 
spectrum") is provided by the method of "crossed spectra," which also 
has already been employed by Stokes (1585). The real image of a 
continuous spectrum is formed on the luminescent surface; only 
certain parts of this spectrum excite luminescence. A second "ana- 



22 



EXPERIMENTAL TECHNIQUE 



lyzing" spectrograph, with its slit perpendicular to the slit of the first 
spectroscope, deviates the light belonging to the primary spectrum 
as well as the luminescence light and thus permits the determination 
of the regions of the primary spectrum by which the various parts of 
the fluorescence spectrum have been excited. The method has also 
been applied, with slight modifications, to the investigation of the 
volume fluorescence of vapors. Furthermore, the method can be applied 
to the determination of the ' 'excitation spectrum" of a slowly decaying 
phosphorescence : when the primary radiation is interrupted, the phos- 
phorescent surface remains luminescent only where the spectrum of 
primary radiation has been able to excite phosphorescence (F, 1631) . 

Sources of light with a continuous spectrum are the sun, the carbon 
arc, tungsten filament lamps, and electric discharges in hydrogen gas 
of about 1 mm pressure. The choice is frequently influenced by the 
spectral region required for a specific experiment ; thus the hydrogen 
discharge alone provides a continuum below 2500A. The light source 
is of particular importance if the resonance radiation of a gas or vapor 
is to be investigated. Since the absorption lines are extremely narrow 
in this case, the primary radiation must have a high intensity at the 
center of the lines and these must be free of self-reversal. Spark 
discharges or high pressure arcs are therefore quite inadequate. In the 
earlier stages of this kind of research, sodium chloride flames and 
mercury arcs of the Hanau type were almost exclusively used. In order 
to keep the vapor pressure at a low value, the mercury lamps, or at 
least their electrodes, were cooled by running water, following a 
suggestion by Kerschbaum (767). Furthermore, the arc was pressed 
close to one of the walls of the tube by a magnetic field so that the 
reabsorption of the lines by a layer of nonluminous vapor was 
minimized (1867). At present these lamps have been almost completely 
supplanted by hot cathode discharge lamps containing argon or neon 
with an admixture of a small quantity of a metal ; by the heat generated 
by the discharge the metal is evaporated and becomes the carrier of 
the light emission. By a suitable choice of voltage and current density, 
90 % of the total radiation of such mercury lamps can be concentrated 
in the line 2537A, practically without self -reversal. Sodium, cadmium, 
zinc, thallium, and magnesium lamps of this type are also available. 

For further suppression of line reversal, Cario and Lochte- 
Holtegreven have constructed a metal-vapor lamp in which the hot 
metal vapor is prevented from distilling out of the high-temperature 
discharge chamber by a continuously circulating stream of a rare gas. 
Simultaneously this gas stream protects the window of the lamp, 



CONTAINERS 23 

which must be kept at a low temperature, against corrosion by the 
vapor or deposit of solid metal {204). 

If it is important for an investigation that the width of the line in 
the primary radiation be narrow and absolutely constant, a "resonance 
lamp" isusedas light source. This isa highly evacuated tube containing 
the vapor of the metal in question and kept at a well-defined tempera- 
ture. The resonance lamp is excited to emit its characteristic 
radiation by one of the light sources which have been described 
above. 

10. Containers. The fluorescence of gases and vapors is investi- 
gated, in general in carefully cleaned and highly evacuated glass or 
quartz vessels. If pressure and temperature of a vapor have to be 
varied independently, a side tube is attached to the observation 
chamber and both are heated by separate electric ovens. The side tube 
must always be kept at the lower temperature in order to regulate the 
vapor pressure. Many metal vapors attack the glass at high temp- 
eratures; for some metals, e.g. sodium, special resisting glasses have 
been developed. If such glasses are not available, metal vessels with 
sealed-on water-cooled windows can be used occasionally. However, 
they are not suitable for precision measurements, partly because of 
the bad definition of the vapor pressure in a volume of varying temper- 
ature, partly because of the unavoidable impurities which are released 
by the hot metal walls. 

For special purposes a molecular beam which is projected from 
an oven through a narrow diaphragm into the observation chamber is 
excited to fluorescence. This method has proved useful, for instance, 
in the excitation of the resonance radiation of lithium vapor, which is 
extremely corrosive for almost all materials. Other applications of the 
method are mentioned in Sections 20, 22, and 23 (32 3). 

The fluorescence of liquids is observed in cuvettes with plane 
windows for the admission of the exciting light. In order to avoid 
scattering of the primary radiation in the direction of observation by 
multiple reflection, the vessels containing a fluorescent gas or liquid 
frequently have the horn-like shape which Strutt (Lord Rayleigh) 
used for the investigation of molecular light scattering (Figure 8a). 

The mode of illuminating a fluorescent gas or liquid depends on 
the problem under investigation. If the luminescence is weak and 
the highest possible intensity must be obtained for spectrographjc 
research, a tubular mercury lamp is placed side by side with the horn- 
shaped tube, both are surrounded by a cylindrical reflector, and an 
image of the luminescent volume is formed on the slit of a spectrograph 



24 



EXPERIMENTAL TECHNIQUE 



which is screened from direct lamp radiation by a suitable set of 
diaphragms (Figure 86). 

If, on the other hand, specific properties of the fluorescence are 
to be determined, as, for instance, its angular intensity distribution or 
its polarization, the exciting light must enter the luminescent medium 





! 




p 


1 














& 


$ 


#» 




a 


\ 


• 


¥y 




S FL 


ip> 






w 




t 


1 








I 1 




p 




5 a t 

Fig. 8. Wood's device for high intensity excitation of fluorescence. 

FL: container of fluorescent solution with hornshaped end ("Rayleigh horn") . 

W: concentric tube for filter and cooling liquids. 

Hg : mercury arc lamps . 

P: elliptical cylindrical aluminum reflectors. 

S : screen with circular diaphragm O . 

as a parallel beam produced by a suitable lens system from a point 
source of light. 

With the exception of glasses, photoluminescent solids are seldom 
available in large transparent pieces. In most cases they form micro- 
crystalline powders. For the investigation of the emission by a single 
microcrystal, the fluorescence must be observed under a microscope. 
In general, the powder is spread out on a porcelain dish or a glass or 
metal plate, and frequently it is fastened to the support by means of a 
binder. Sometimes it is advisable to keep the luminescent screen in an 
evacuated chamber in order to avoid photochemical reactions with 
the surrounding gas. 



PART I 
Fluorescence of Gases and Vapors 



CHAPTER I 

MONATOMIC GASES AND VAPORS 

A. Nomenclature of Series Spectra 

11. Quantum Numbers. Only the most loosely bound electrons of 
an atom participate in the optical absorption and emission processes. 
For practically all spectra which are treated in this chapter, a single 
electron acts as "emission electron" ("Leuchtelectron" in Sommer- 
f eld's terminology). The energy contributed by an individual electron 
to the total internal energy of an atom is determined by 5 quantum 
numbers n, l,f,j, and m. In Bohr's original atomic model, the "princi- 
pal quantum number" n defines the length of the major axis of the 
elliptical orbit on which the electrons move around the positive 
nucleus. The values of n are 1, 2, 3, 4 . . . The secondary quantum 
number / measures the orbital angular momentum of the electron in 
units of h/2-rr and can be equal to any integral number between and 
n~\. If an atom contains several electrons outside its outermost closed 
electron shell, the secondary quantum number of the atom L is ob- 
tained by vectorial addition of the I values of the individual electrons.* 
For all spectra occurring in this chapter, I differs from zero only for 
the emission electron ; hence L is always equal to I. (The total contri- 
bution of all electrons in the inner shells toward L is zero.) 

Every individual electron has a spin quantum number s = 1/2; 
vectorial addition of these individual spin values yields the total 
electronic spin of the atom 5, so that 5 = 1/2 for one outer electron, 
5 = or 5 = 1 for two electrons, S = 1/2 or S = 3/2 for three 
electrons, etc. 

By vectorial addition of I and s or L and 5, respectively, the 
"inner" quantum number; of the individual electron or / of the.atom 
(measuring the resultant electronic angular momentum) is obtained 

\L—S\<J<L + S (13) 

There are, in general, (25 + 1) different values of / for L > S and 
(2Z. + 1) values of / for L < S. 

* This so-called Russell-Saunders coupling prevails for all spectra which 
are considered in the followng sections. 

27 



28 MONATOMIC GASES AND VAPORS 

/ is the "hyperfine structure" quantum number. It is the vectorial 
sum of J, as denned above, and of i, the momentum of the nuclear 
spin, and corresponds to the total angular momentum of the atom. 
For elements of even atomic number, i is, with very few exceptions, 
equal to zero; but for "odd elements," i = 1/2, 3/2, etc., according 
to the number and nature of the elementary particles (protons and 
neutrons) constituting the nucleus. Thus : 

I/— *'l </</ + * ( 14 > 

and there are (2i 4- 1) different values of f, it J > i and (2/ + 1) 
values if / < i. 

Finally, the "magnetic quantum number" m determines the 
angular momentum which is produced by the precession movement 
of an atom revolving around the lines of force of a magnetic field 
and therefore m determines the orientation of the atom in space. 
Since: 

—f<m<f (15) 

there are always (2/4- 1) values of m. For even elements with no 
nuclear spin, / is equal to / and, therefore : 

—J<m<J (15a) 

with (2/4-1) different values of m. Relation (15a) replaces (15) quite 
generally, even for atoms with * > 0, if the applied magnetic field is 
so strong that its influence prevails over the influence of the magnetic 
field produced by the nuclear spin ("Paschen-Back effect" of the 
hyperfine structure). 

12. Energy Terms. The major part of the energy characterizing 
an atom in a specific state (n, L, J,f, m) is determined by the value of 
n. An energy level corresponding to a given value of n splits into several 
sublevels originating from the fact that the other quantum numbers 
can contribute an additional energy. These additional energies de- 
crease, in general, in the order in which the quantum numbers are 
enumerated above. The magnetic quantum number causes the splitting 
of an energy level into various "Zeeman levels" only if an external 
magnetic (or electric) field acts on the atom. In the absence of such 
fields, the atom is "degenerate" with respect to spatial quantization. 
However, although the sublevels corresponding to various possible 
values of the quantum number m coincide energetically, their multi- 
plicity determines the statistical weight of the state. 

The energy differences between the sublevels corresponding to 
the hyperfine structure are so small in many cases that they need not 



ENERGY TERMS 29 

be considered for most spectroscopic research work. Therefore, the 
first three quantum numbers are sufficient, in general, for the con- 
struction, of the energy term scheme of an element. Each term is 
characterized by a symbol of the form: n'Sj, n r P J: etc. n and J have 
the meanings explained in the preceding section and r indicates the 
multiplicity of the term, i.e., the greatest number of values which / 
can assume according to Equation (13). Instead of stating the quantum 
number L explicitly, the symbols S*. P, D, F, etc., are used for 
L = 0,1,2, 3, etc. Thus the various terms are denoted as ^S-terms 
(singlet 5-terms), 3 P-terms (triplet P-terms), etc. / has only a single 
possible value in a singlet term, it has two possible values in a doublet 
term, etc. According to the definition, / is an integer number (J = 
0, 1, 2, 3 . . .) for odd values of r (singlets, triplets, etc.) and a half- 
number (J = 1/2, 3/2, 5/2 . . .) for even values of r (doublets, quartets, 
etc.). L being equal to zero for 5-terms, these are always single, even 
if they belong to a doublet or triplet system, since for L < S the multi- 
plicity is: 2L + 1. 

The monovalent elements in the first column of the periodic 
system have only doublet terms, those in the second column, with two 
external electrons, have singlet and triplet terms, those in the third 
column have doublet and quartet terms, etc. 

Since the principal quantum number n must always be larger 
than L, only the series of S-terms begins with n = 1, the P-series 
begins with n = 2, and the Z)-series with n = 3. At first it was usual 
to designate the lowest state of an atom, if it was an 5-state, by the 
symbol 15, and the following states were then called 2P, 25, 3D, etc. 
Similarly, the ground state was called 2 P if it corresponded to a P- 
term. In more recent papers on spectroscopy, however, the correct 
notation is used exclusively and the principal quantum number n of 
the emission electron in the ground state is determined by the number 
of electrons that are contained in the interior shells. Only the ground 
state of the hydrogen atom and of the helium atom is called 15, the 
ground state of lithium is 25, and that of sodium 35. In Table 1, the 
two modes of designations are collected for all elements dealt with in 
this book; it may serve for comparing earlier publications with more 
modern papers. 

Instead of the energy-level diagrams of Figure 1, diagrams like 
those of Figure 13, 15a, 17 (so-called Grotrian diagrams) are used for 
representing the complete set of terms of an atom. The series of terms 

* The generally accepted use of the same symbol S for the total electronic 
spin and for terms with L = can never be misleading. 



30 



MONATOMIC GASES AND VAPORS 



Table 1 

Main Quantum Numbers for the Lowest S-, P- and D-Terms 

of All Atoms Fluorescing in the Gaseous State 



Old 










designa- 


IS 2f> 3D 


l.S IP 3D 


IS IP 3D 


IP 3S 3D 


tion 












Li 


2S IP 3D 


He 


IS 2P 3D 


Ca 


45 AP AD 


In 


5P 6S 5D 




Na 


35 3P 3D 


Ne 


2S IP 3D 


Zn 


AS AP AD 


Tl 


6P 7S 6£> 




K 


4S AP AD 


A 


3S 3P 3D 


Cd 


55 5P 5D 


Pb 


6P 75 6Z> 


igna- 
tion 


Cu 
Ag 
Rb 
Cs 


45 AP AD 
5S 5P 5D 
55 5P 5D 
6S 6P 6£> 


H 


IS 2P 3D 


Hg 


65 6P 6D 







for which n increases, while L and / are kept constant, are plotted in 
a vertical column as short horizontal lines ; the various columns for 
different values of / and L are plotted side by side. The vertical 
distances between the individual short lines are again proportional to 
the energy differences between the terms, measured in eV or cm -1 . 

13. Series Lines. A spectral line is determined by two terms, for 
instance, 3 X 5 and 5 1 P 1 . If only the frequency of the line is to be 
stated, it is given by the difference 5 1 P 1 -3 1 5 ; if the direction of the 
transition is to be made clear, the dash is replaced by an arrow. 
According to the footnote on page 4, n"P^-n'S represents an 
emission process and n"P+- n'S represents an absorption process. 

For deriving the lines which actually occur in the spectrum of an 
atom, knowledge of the terms does not suffice : it must be supplemented 
by knowledge of the "selection rules." Only transitions are "allowed" 
for which: 

An = 0,1,2,3 . . ., and simultaneously: 

AL = ± 1 and AJ = or ± 1. 

The selection rules for the hyperfine-structure quantum numbers and 
for the magnetic quantum numbers are : 

Af = or ± 'l and Am = Opr ± 1. 

Only if / = 0, transitions with AJ = are forbidden ; under these 
conditions, AJ = + 1 is the only allowed transition. This is particu- 
larly important because of the resulting metastability of the 6 3 P -state 
of mercury and of the corresponding states of other elements. Am = 
is forbidden for the magnetic quantum number if AJ = for the line 
under consideration, as, for instance, for a 3 P 1 - 3 5 1 transition. It has 
already been mentioned in the introduction that forbidden transitions 



SERIES LINES 31 

do actually occur, though with very small probability. (The transition 
A] = for / = practically does not occur at all.) 

It follows from the selection rule AL = ± 1 that the only allowed 
transitions from an 5-term are those to a P-term, from a P- to an S- 
or a D-term, and, generally, from one vertical column in a Grotrian 
diagram to the neighboring columns, if terms which differ only by 
their /-values are classified as belonging to the same column. 

[This simple formulation of the selection rule for AL suffices for 
all atomic spectra if I differs from zero for only one electron outside of 
the completely closed shells (for instance, the spectra of Na, Hg, Tl 
and other elements of the first three columns of the periodic system, 
and also for the spectra of the rare gases). If several electrons have 
/-values greater than zero for instance, if an atom contains two or 
more ^"-electrons (with 1=1) one must apply the more general 
quantum-mechanical law according to which only transitions between 
"even" and "odd" states are allowed. A state is even when the alge- 
braic sum Zl is even, and .the state is odd when this sum is odd, odd 
states being characterized by a superscript ° as in 3 P± , in contrast to 
an even state 3 P V The atom of lead has two &p electrons in its even 
ground state 3 Pj ; if one of these electrons is raised to the level 7s, an 
excited odd 3 Pj° state is formed. Transitions between these two 
3 P-triplet states are allowed if they agree with the selection rules for 
AJ. The fluorescence spectrum of lead vapor (Figure 10) provides the 
only instance mentioned in this chapter for a transition of this kind.] 

If a term combines successively with all terms of a neighboring 
column in the Grotrian diagram so that the L-value of the latter is 
kept constant while the n- values vary, a "series" of lines is obtained, 
as, for instance, the series 6P-6S, 7P-6S, 8P-6S, etc. If, on the* other 
hand, all quantum numbers with the exception of J are kept constant 
in the initial and the final state, while all possible values are assigned 
successively to / in both states, the resulting lines form a multiplet, 
as, for instance, 6 3 Z) 1|2>3 -6 S P 0>1|2- 

"Intercombination transitions," as, for instance, those from a 
triplet state to a singlet state, have small probabilities, in general. 
They are strictly forbidden in the spectra of the lightest elements, but 
become more probable with increasing atomic number'of the elements. 
In the spectrum of mercury the intercombination resonance line 
3 P 1 - 1 5 is relatively strong, the analogous lines in the spectra of Cd 
and Zn are much weaker, and, in the spectrum of helium, intercombi- 
nation lines between the triplet and singlet systems (ortho and 
parhelium spectrum) do not occur at all. Simultaneously, the sepa- 



32 MONATOMIC GASES AND VAPORS 

ration of the individual triplet terms becomes smaller as compared 
with their mean distance from the corresponding singlet term. 

The series originating from the transitions PS (S being the 
ground state of the atom) are called the principal series, those corre- 
sponding to transitions D—P are the diffuse, and those corresponding 
to the transitions S-P are the sharp secondary series. 

At moderate temperatures, at which practically all atoms are 
in the ground state, only the principal series or the two secondary 
series appear in the absorption spectrum, if the ground state is 
characterized by an S- or a P-term, respectively. 

Each series of terms converges towards an upper limit corre- 
sponding to the energy needed for the ionization of the atom in a 
given initial state. In the same way, every absorption series converges 
towards a short wavelength limit, beyond which a region of continuous 
absorption begins. Absorption of light in this continuous region leads 
to the photoelectric ionization of the atom. 



B. Fluorescence Lines 

14. Resonance Lines. Pure resonance radiation, as exclusive 
re-emission of absorbed monochromatic light, occurs only if there is 
no other possible spontaneous transition from an excited state than 
the return to the ground state. Therefore, the ground state must be 
single, a condition always fulfilled if the ground state is a S-state. 
This is the case for all metals of the first and second columns of the 
periodic system. It is not necessary, on the other hand, that no other 
levels exist between the excited and the ground states, as long as 
spontaneous transitions of the electron into any existing intermediate 
levels are forbidden by the selection rules. Excited states of this type 
are characterized for the alkali metals by the term symbols P 1/2 and 
P 3 j 2 , and for the metals of the second column of the periodic system 
by ^and 3 P ,i, 2 ; transitions 2 P 3/2 ^ 2 P 1/2 , ^i^^o.vi 01 sp i ■* 3p o 
are forbidden (compare Figures 1 3 and 15). It follows that an atom can 
have more than one genuine resonance line. Thus, either of the 
D-lines of sodium is a resonance line ; if the primary radiation contains 
in its spectrum only one of these lines, and if the vapor pressure is 
sufficiently low so that no collisions occur during the lifetime of the 
excited state, only this component of the doublet is re-emitted by the 
vapor (i8g5)'. Resonance emission of the first doublet of the principal 
series has also been observed in the vapors of lithium (6708A, without 



RESONANCE LINES 



33 



resolution of the two components which are separated by a distance 
of only JA), as well as in the vapors of potassium (7699 and 7645A) 
and of silver (3382 and 3280A) {127,1133). (Compare Section 94 
concerning the excitation of resonance radiation of copper.) 

The two resonance lines corresponding to the transitions a P 1 ->■ x 5 
and X P X ->- ^o, which have been observed in the vapors of several 
metals of the second column of the periodic system, are collected in 
Table 2. The mercury line 1849A coincides with the first strong 

Table 2 

Resonance Lines of Metals Belonging to the Second Column of 

the Periodic System 

(Wavelength in A) 



M 


Hg 
6 


Cd 
5 


Zn 
4 


Ca 
4 




2537 
1849 


3261 
2288 


3076 
2139 


6537 


w 1 P 1 - « 1 S 


4227 







l£H- 



absorption bands of 2 ; therefore, it is observed only if the primary 
and the secondary radiation do not have to pass through more than a 
few centimeters of atmospheric air. Resonance excitation of this line 
so far, has been treated only in one paper {1395). On the other hand, 
the intensities of the long-wavelength resonance lines of Cd, and even 
more of Zn, are rather weakbecause of the small transition probabilities 
(111-113,1251,1524,1531,1540) . 

While the metals enumerated above are the only ones in whose 
vapors resonance radiation has 
actually been observed, there is 
no doubt that the other elements 
of the first columns of the periodic 
system would behave the same 
way under adequate conditions. 
The experimental difficulties are 
caused either by the high temp- 
eratures needed for the product- 
ion of sufficient vapor pressure 
(as in the case of gold or barium 
and strontium) , or by the fact that 
the resonance lines are situated 
in the far u.v., which is accessible 
only to vacuum spectroscopy (as 
in the case of the rare gases or atomic hydrogen). 

Pringsheim 2 



6 *£>!*--= 
6 2 0%^ 



7 Z S,, 



5 ^/ 2 



6 2 /\i 



eV 
5.04 
4.65 
4-35/33 



3.18 



0.96 



Fig. 9. Level diagram for the fluo- 
rescence of Tl [Mueller (1084)]. 



34 



MONATOMIC GASES AND VAPORS 



15. Multiple Ground States. If the ground state of an element is 

a doublet state, resonance radiation, in the strict sense of the word, 

cannot occur. A typical example is provided by thallium. The lowest 

energy level of the thallium atom is characterized by the symbol 

6 2 P 1/2 . By absorption of the lines 3776 and 2768A, the atom is raised 

into the states 7 2 S 1/2 and 6 2 Z> 3/2 , respectively (Figure 9). Transitions 

between these two levels are forbidden, but transitions from either 

are possible to 6 2 P 3/2 as well as to 6 2 P 1/2 . Therefore, the lines 5350 or 

3529A, respectively, appear simultaneously with the exciting lines in 

the fluorescence spectrum. At 
— 4.35 «/ 



3 1° 



Fig. 10. Level diagram for the fluo- 
rescence of Pb (Winans) . 



high temperatures some atoms are 
in the state 6 2 P 3/2 , when thermal 
equilibrium is established, though 
the relative concentration is low 
(about 10-* at 800° C) because of 
the large energy difference of 0.96 
eV between the two doublet P- 
levels. Nevertheless, the fluores- 
cence emission of the lines 5350 
and 3776A can be excited under 
these conditions -by irradiating 
Tl-vapor with the green thallium 
line as well as with the ultraviolet 
line 3776A. In either case, the 
absorbing atoms are raised to the 
level 7 2 5 1/2 while the initial state is 6 2 P 3/2 or 6 2 P V2 . The relative in- 
tensities of the two emission lines are, as might be expected, indepen- 
dent of whether the vapor is excited by the green or the u.v. line. 
At temperatures below 500° C, irradiation with the green line is 
practically ineffective in producing any fluorescence, as has been 
shown by Terenin (1631). 

The term system of indium is strictly analogous to that of 
thallium (Figure 53). The resonance radiation of indium has never 
been investigated in laboratory experiments. However, the great 
intensity of the indium line, 451 1A (6 2 S 1/2 -5 2 P 3/2 ), in the spectra of 
certain variable stars has been interpreted by Thackeray as being 
caused by resonance excitation : the hydrogen line Hy (4101 .735 A) coin- 
cides almost exactly with the indium absorption line, 4101. 7A (6 2 5 1/2 - 
5 2 -Pi/2), and the Balmer lines of hydrogen are always very strong in the 
spectra of these stars (1650) . 

Results similar to those obtained with thallium vapor were found 



MULTIPLE GROUND STATES 



35 



by Terenin for the vapors of lead, bismuth, and antimony ; the term 
schemes of these metals were then not completely analyzed and 
the investigation of their fluorescence made it possible to decide which 
lines were able to excite luminescence and were therefore absorption 
lines of the atoms in the ground state, and which lines occurred 
simultaneously in the fluorescence spectra and were therefore emitted 
from the same excited level. By means of the method of "crossed 
spectra" all these problems could be solved in a single experiment. 
The absorption and emission lines found by Terenin in this way are 
shown in Figures 9-12 (1631). 



t 




r- 

CVJ 


00 
(£> 
O 
IO 


CM 


> 




1 


■ 





4 


P-i 








1 


\, 


V,-^ 


2 




, 






'■*■ 


i 






CO 

r» 
co 

CO 


CJ 


CM 


O 

r-- 

CVl 


<0 
C\J 


CO 

en 
m 


CO 
(0 
O 
CM 










_J 


' 


' ' 




z n —5 


1 - 










t>3 










2„ 










> 


' ' 



Fig. 11. Level diagram Fig. 12. Level diagram for the fluo- 

for the fluorescence of rescence of Sb (Terenin) . 

Bi (Terenin J. 

Furthermore, Terenin observed the As-lines 2288 and 2381 A, 
when As-vapor was irradiated with the full radiation of an As-arc; 
however, he was not able to determine the wavelength of the light 
which was responsible for the excitation. Finally, re-emission of 
atomic Mn-lines was observed, when manganese vapor was illuminated 
with the light from a manganese spark (437). The fluorescence spectrum 
consisted of two narrow triplets at 4032 and 2798A ; the former could 
even be resolved into its components (4030.76, 4033.07, 4034.49A). 
According to Catalan, these triplets are caused by the transitions 
3 P 01?2 ^- 1 S and 3 P '0,1,2 "* x ^o (437)- However, the exciting lines 
emitted by the Mn-spark were probably self-reversed, and since the 
same fluorescence could be produced by the radiation from sparks 
between copper, zinc, or chromium electrodes, it must be assumed 
that in this, as perhaps also in some of the other cases mentioned 
above, the fluorescence was not due to a direct excitation of the atoms 
but to excitation of diatomic molecules with subsequent emission of 
atomic lines (compare Section 69) . 



36 



MONATOMIC GASES AND VAPORS 



16. Excitation by Absorption of Lines Leading to Higher Energy 
States. It has been assumed, so far, that the vapors were excited by 
absorption of the first line of their absorption series. If other lines of 
this series are used for the excitation, a number of energy levels must 
exist between the excited and the ground states, so that the "emission 
electron" need not return to the ground state by the same way by 
which it reached the excited state; the return can be achieved in 

several steps, and consequently several 
new lines may be observed in the emission 
spectrum. This phenomenon has been in- 
vestigated most thoroughly in cesium vapor 
by Boeckner. The Cs-line 3889A, corre- 
sponding to the transition 8 2 P 1/2 <- 6 2 S 1/2 , 
coincides so closely with a strong line of 
the helium spectrum that this transition 
can be stimulated by irradiating cesium 
vapor with the light from a helium dis- 
charge tube. Apart from the re-emission of 
the same line, a number of other lines are 
obtained under these conditions in the 
fluorescence spectrum of the vapor. These 
lines, among which the resonance line is 
to be found, are marked in the diagram 
of Figure 13 by heavy arrows. The missing 
5 p P D *D f-yF unes w h ien are necessary for completing 
y T 1 I i i i the transition from 8 2 P 1/2 to the ground 

^ „ „ , . ,. state via the intermediate levels 75 and 

Fig. 13. Grotnan diagram , j • .i_ j- x. j u j 

for the fluorescence of Cs. 77) are marked in the diagram by dotted 

arrows. They do not appear on the spec- 
trograms because of their great wavelengths, but they are certainly 
present in the emission spectrum. This is also true for the second 
component of the resonance doublet 8943. 5A (6 2 P 1/2 -+ 6 2 S 1/2 ), while 
the second component of the doublet 8 2 P 3/2 -> 6 2 S 1/2 actually cannot 
be emitted, because the transition 8 2 P 3/2 ^- 8 2 P 1/2 does not occur (125). 
The presence of the D-lines in the fluorescence spectrum of sodium 
vapor irradiated with the line 3303A had been observed by Strutt 
(Lord Rayleigh) much earlier {1 593,1594)- This line is one of the 
components of the second doublet of the main series of sodium and 
corresponds to the transition 4 2 P 1/2 -3 2 S 1/2 . It coincides sufficiently 
closely with the zinc line 3303. 7A, which could be used for the purpose 
of exciting the sodium vapor. It was this observation which induced 





9- 




■9 




9- 




sPl 


;8 83 


8- 


8" 


i< "" j 


/ / 


' In 
*i I] 


7- 
-7 


7- 


11/ sj 

Ml '< 
1/ // 
// 4r 


l 


1 6- 

^6 




6- 











EXCITATION BY ABSORPTION OF LINES 



37 



Bohr to assume that a stepwise return to the ground state is not 
effectuated directly over a forbidden transition (4P->3P), but via 
intermediate levels like 4S or 4Z>. In Strutt's experiment, which was 
executed in vapor of relatively high pressure, the transition 4P -» 3P 
might have been caused by collisions and this explanation seemed 
even to be made plausible by the great width of the D-lines, which 
would then have been caused by the Doppler effect. However, such an 
interpretation can no longer be upheld from the theoretical viewpoint, 
and later experiments which were performed at lower vapor pressures 
gave the same results with regard to the emission of the D-lines without 
showing an unusual broadening of the lines {i34°) ■ 

If thallium vapor is illuminated with the full radiation emitted 
by a thallium lamp, many higher series lines are observed in the 
fluorescence spectrum. These lines and the corresponding transitions 
are collected in Table 3. Since the spectrograms were obtained without 

Table 3 

Fluorescence Spectrum of Thallium Excited by the Radiation 
from a Thallium Lamp 



Wavelength in A . . 


5350 


3775 


3529 


Transition . . . 




72S l/2 -62P 3/2 


73S l/2 -6 2 P l/2 


6*D lh -e*P ll2 


Wavelength in A . 




3519 


3230 


2922 


Transition . . . 




6^ 5/2 -6^P 3/2 


82S l/2 -6"P 3/2 


72D 3/2 -6*P 3/2 


Wavelength in A . 




2918 


2768 


2580 


Transition . . . 




7 2 D 5 / 2 -6*P 3/2 


6*D 3/2 -6*P l/2 


S^-VP^ 


Wavelength in A . 




2380 






Transition . . . 




VDjg-VPilt 







spectrai resolution of the primary radiation, it is impossible to de- 
termine which of the individual lines were stimulated by light of the 
same wavelength and which were due to stepwise emission. 

Fluorescence can be excited in He by the radiation from a hot 
cathode discharge in helium gas at a pressure of about 1 mm ; the ob- 
servation chamber must be separated from the discharge tube by a 
window which is transparent to short-wavelength u.v. Lee's and 
Skinner's earlier experiments have been confirmed by Maurer and 
Wolf. They obtained numerous lines of the parhelium spectrum 
(singlet spectrum of He; compare the term diagram of Figure 17). 
The lines 5015 and 2964A are the strongest in the fluorescence 
spectrum, the line 3819 is somewhat weaker (3 1 P 1 , 4 x Pi and 5^ -> 
2 1 S ) ; in this case atoms can be transferred by absorption of light 



38 MONATOMIC GASES AND VAPORS 

exclusively to ^-states because deviations from the selection rules 
do not occur. The fact that a few rather weak lines starting from D- 
levels and a few lines belonging to the orthohelium system were also 
observed, was, according to the authors, due to collisions of the second 
kind (8y6,8yy,ggo,ggi). (Compare also Section 19). 

In the emission spectra of particular stars in nebulae, the ortho- 
helium lines have an anomalously large intensity as compared to the 
parhelium lines. It is assumed that this abnormal intensity distribution 
is due to the fact that only the lines of the singlet system are excited to 
fluorescence by absorption of the underlying continuous radiation. 
When the emission is due to recombination of helium ions with 
electrons, the singlets are much weaker than the triplets [i4y-i4g). 

Lau and Reichenheim ascribe a strong emission of the Balmer 
lines Ha and Hy (2P -* 25 and 3P -> 25) in a hydrogen discharge 
tube to a fluorescence excitation caused by the absorption of the corre- 
sponding Lyman lines (2P-»- 15 and 3P -+ IS) in normal hydrogen 
atoms. Ah excitation by collision with electrons seemed to be impossible 
under the experimental conditions. Phenomena of this type may be 
rather frequent in gas discharge tubes, if light emission is observed in 
the space outside of the path of the discharge itself (corona) {86g). 

Astrophysics provides other examples of a stepwise return from 
an excited state reached by irradiation, and of the correspondent 
emission of several lines by the excited atoms. The spectra of nebulae 
contain certain groups of lines of relatively high intensity, the origin 
of which was unexplained until Bowen realized that they belong to 
doubly ionized oxygen and nitrogen (O III and N III). The line pro- 
ducing the excitation of oxygen is the He Il-line 303. 78A. The 
complete course of the absorption and emission processes can be 
easily understood by means of the diagram of Figure 14, in which all 
actually observed oxygen lines are rendered by heavy arrows. The 
resonance between the He-line and the absorption line of O III is 
complete if the Doppler width is taken into account . A similar resonance 
exists between the emission line 374.436 of O III and the absorption 
doublet 374.434/442A of N III, which explains the subsequent exci- 
tation of the lines of N III indicated in the right-hand part of the 
diagram of Figure 14 (148). 

17. Stepwise Excitation. If an atom is raised to an excited level 
by some mechanism for instance, by the absorption of the resonance 
line, or by the collision of the atom with an electron it is able to absorb 
lines belonging to new series starting from that excited state, before 
it returns spontaneously to the ground state. These new absorption 



STEPWISE EXCITATION 



39 



he normal absorption spectrum of the atom, and 

" states reached by this process a great number 

■\ be emitted as fluorescence. This process can 

times: the levels reached by the emission of 

"e the starting points of new absorption 

1 to the emission of tertiary fluorescence 




yp, 



level diagram of O III and N Ill-lines in the spectra 
of stellar nebulae. 



: intensities of the tertiary lines are small, in general, unless 

.ondary emission brings the atom into a metastable state, as, 

instance, the states 6 3 P or 6 3 P 2 of mercury (Figure 15). In the 

xosence of other perturbations the atoms must remain in these 

metastable states until they are dislodged from them by the absorption 

of radiation. 

Stepwise excitation was discovered by Fuechtbauer in mercury 
vapor (452) and has been investigated extensively by Wood, who used 
a much improved experimental setup. The mercury vapor is contained 
in the quartz tube R (Fig. 16 a) and is excited by the resonance 
radiation of a cooled mercury arc lamp I. The second mercury lamp II 



40 



MONATOMIC GASES AND VAPORS 



is not cooled and is unable to excite resonance radiation because of 
the self-reversal of the line 2537A in its emission spectrum. As Fuecht- 
bauer has shown, lamp II produces no effect at all in tube R, unless 
some of the mercury atoms in R are transferred into the state 6 S P 1 by 




TRIPLET SYSTEM 



SINGLET SYSTEM 



Fig. 15. Grotrian diagram for Hg. 



the radiation from lamp I. If, on the other hand, the total radiation of 
lamp I alone is used for excitation, all transitions shown in Figure 
15 by solid lines are observed in the fluorescence of R. Various 
combinations of exciting lines can be selected by interposing filters 
between R and the two lamps; as soon as the resonance line is con- 
tained in the spectrum of the primary light, all lines which can be 
expected are present in the fluorescence spectrum. The relative in- 



STEPWISE EXCITATION 



41 



tensities of these lines depend to a large extent on the nature of the 
lines which are transmitted by the combination of filters used. The 
triplet 6 3 Z) li2 , 3 ->6 3 P 2 , with the wavelengths 3663, 3655, and 3650A, 
may be discussed as an example. For producing secondary fluorescence 
of any appreciable intensity, the exciting radiation must contain, in 
addition to the resonance line, at least one of the lines 3131, 3126, or 




Fig. 16a. Wood's setup for the ob- 
servation of stepwise excitation of 
mercury fluorescence. 

I: water-cooled Hg-lamp. R: 
resonance lamp. S: slit of 
spectrograph. 77: hot Hg- 
lamp. Fj and F 2 : filters. 




Fig. 16b. Stepwise excitation of the 
u.v. Hg-triplet (R. W. Wood). 

(1) excited by Hg-radiation of 
I < 4000A. "(2) excited by Hg- 
radiation including the line 
4358A, 



4358A, all starting from the level 6 s P v Other transitions starting from 
this level correspond to absorption lines of relatively small intensity. 
If light of all wavelengths above 4000A is removed from the spectrum 
of the primary radiation by means of filters, ' 'secondary absorption" of 
the lines 3131 and 3126 raises the atoms from the state 6 3 P t to the 
states 6 3 D t and 6 3 D 2 , from where the triplet lines 3663 and 3655A 
can be emitted. By these emission processes, atoms reach the meta- 
stable state 6 3 P 2 and are now able to absorb in a tertiary process all 
three of the triplet lines and eventually to re-emit them again. This 
tertiary emission, however, is very much more improbable than the 
secondary processes, and, furthermore, the initial state from which 
it starts is produced by the secondary emission of the two other 
Pringsheim 2* 



42 MONATOMIC GASES AND VAPORS 

triplet components only. Therefore, the intensity of the third com- 
ponent of the triplet (3650A) is very low as compared with the two 
others. If the line 4358A is transmitted through the niters, atoms 
are raised b.y absorption of this line to the level 7 3 S X and subsequently 
drop by secondary fluorescence emission of the line 5461 A to 6 3 P 2 . 
From there, they are able to absorb any one of the three triplet lines 
and thus to reach the states 6 3 D V 6 3 Z> 2 , or 6 3 D 3 ; the only possible 
transition from 6 3 £> 3 is to 6 3 P 2 , while the atoms can leave the two other 
6 3 Z)-levels by several allowed transitions. Accordingly, the line 
3650A is now the strongest of the triplet in the fluorescence spectrum 
(462,1889,1903) (Fig. 16b). 

These theoretical results, as well as other conclusions derived from 
the selection rules, are in good agreement with Wood's photometric 
measurements. Simultaneously with the triplet component 3663A, 
the "intercombination line" 5769A, corresponding to the possible, 
though little probable, transition e 3 ^ -> 6 1 P 1 , was obtained by Wood, 
with relatively small intensity. Other intercombination lines, 6 l D 2 -> 
6 3 P 2 (3662.9A)or7 1 S ->6 3 P 1 (4078A), were observed in the secondary 
fluorescence spectrum of mercury vapor by Terenin, who employed an 
experimental arrangement similar to the one used by Wood (1631). 

If fluorescence is excited stepwise, the intensity distribution in 
the emission spectrum must depend on the relative intensity of the 
lines in the primary radiation and its modification by the use of 
selective screens. If the total intensity of the primary radiation is 
altered, for instance, by increasing the distance between the arc 
lamp and the fluorescence tube, or by interposing a wire-gauze filter, 
only the intensity of the primary resonance radiation is proportional 
to the first power of the intensity of the exciting radiation, while the 
intensity of the "secondary lines" (e.g. 3655A) varies with the square, 
and that of the "tertiary lines" (e.g. 3650A) varies with the third 
power of the primary intensity. 

In the presence of foreign gases, especially of nitrogen, mercury 
atoms which have been raised to the state 6 3 P 1 by absorption of the 
resonance line are transferred into the contiguous state 6 3 P by 
collisions with the molecules of the foreign gas. (The mechanism of this 
process is dealt with in Section 37). The state 6 3 P being metastable, 
a relatively large number of atoms remains in this state. Therefore, 
the absorption lines which originate from 6 3 P have great intensity 
and the fluorescence excited stepwise by the full radiation of a 
mercury arc is much stronger under these conditions than in pure 
mercury vapor. Table 4 reproduces some of the values published by 



STEPWISE EXCITATION 



43 



Wood comparing the intensities of lines obtained in pure mercury 
vapor and in the presence of about 2 mm of nitrogen (i88g). 

Table 4 

Ratio of Intensities (k) of Mercury Fluorescence Lines Excited 

by the Total Radiation of a Mercury Arc in Pure Mercury Vapor 

and in the presence of 2 mm nitrogen 



Final state 


6»P S 


6»P, 


6 a P 


Initial state 


A (A) 


A" 1 


A (A) 


k- 1 


I (A) 


k- 1 


7 3 S 1 


5461 


32 


4358 


16 


4046 


8 


8 3 S! 


3341 


5 


2894 


8 


2753 


16 


63.D! + &D t 


3663 


4 


3131 


16 


2967 


4 


&D 2 


3654 


1 


3126 


2 


— 


— 


&D 3 


3650 


16 


— 


— 







For a complete interpretation of these intensity ratios, a very 
thorough discussion of the experimental conditions prevailing in 
every instance is necessary. Gaviola, who treated the problem, found 
that the observed results could be explained in every case by plausible 
assumptions (462,1716,1903). For instance, an increased emission of 
the line 5641A increases the number of atoms in the metastable state 
6 3 P 2 ; the 6 3 P 2 -atoms can be excited once more and thus contribute to 
some new emission process with an intensity proportional to a higher 
power of the primary radiation. Furthermore, the reabsorption of 
some of the fluorescence lines by the mercury vapor is not quite 
negligible; and finally, a certain amount of genuine quenching (com- 
plete loss of energy) caused by multiple collisions of metastable atoms 
with the foreign molecules may occur. With pure nitiogen, however, 
such collisions do not seem to be of great importance, since Wood was 
able to observe fluorescence emission of the "forbidden" line 2665.8A 
(6 3 P -> 6^0) in the presence of several mm of nitrogen. Because of 
the low transition probability, this line can be emitted only if the 
unperturbed life of the metastable atoms is comparitively long. The 
intensity of the forbidden line is proportional to the intensity of the 
resonance line in the primary light ; its appearance is caused by a single 
process of absorption (1902). (For more details concerning the forbidden 
line compare Section 22). 

Bender observed stepwise excitation of fluorescence in cadmium 
vapor : the results were analogous to those obtained by Wood in pure 
mercury vapor. When excited by the total radiation of a cadmium 
lamp, the fluorescence spectrum contained, apart from the resonance 
Pringsheim 2** 



44 MONATOMIC GASES AND VAPORS 

line 3261 A (5 3 P 1 -> S^S,,), many lines originating from the higher 
excited states. Among these, the secondary lines starting from the 
levels which are reached directly from 5 3 P 1 were again much more 
intense than the tertiary lines. It is noteworthy that in Bender's 
Cd-spectra all lines belonging to the singlet system are missing: 
because of the small probability of intercombinations in the case of 
cadmium, these lines should be emitted almost exclusively, if cadmium 
atoms undergo stepwise excitation after having reached the state 
5^. However the short life of that state, caused by the great tran- 
sition probability 5 x Pj -+ 5%, reduces the probability of absorption 
processes which otherwise would originate from it (gi). 

This interpretation does not agree with Bender's observation 
that in zinc vapor excited by the total radiation of a zinc arc, the blue- 
green triplet 5 3 S 1 ->4 3 P 0tl2 (4810, 4722, 4680A) and the red singlet 
line 4 X Z) 2 -» 4 X P X (6362A) have practically the same intensities. It is 
possible, however, that in this case the short lifetime of the state 4*P X 
is compensated by the very small probability of the transition 
4 3 P 1 <- 4 1 5 . The primary stages in the stepwise excitation of the 
triplet lines and of the singlet line can only be the states 4 3 P 1 and 
4 1 P 1 , respectively. 

If thallium vapor is irradiated with the line 3776A at a tempera- 
ture low enough so that there are practically no 6 2 P 3/2 -atoms in 
thermal equilibrium, the excited atoms are partially transferred into 
this metastable state by the emission of the green line 5350A (Figure 
9). However, the vapor cannot be excited, under these conditions, to 
secondary fluorescence by absorption of the lines 3519 and 3529A 
(6 2 A/2>3/2 -*- ^PyJ), nor do these lines acquire an appreciable intensity 
in the absorption spectrum of the vapor. Thus, the life of the metastable 
state 6 2 P 3/2 of thallium seems, even at low vapor pressure of the order 
of 10~ 4 mm, to be short as compared with that of other metastable 
atoms {1084) . (Compare footnote, page 45) . 

18. Combined Electrical and Optical Excitation. In principle it 
makes no difference whether in stepwise excitation the first stage is 
attained by light absorption or by electron collision. An electric low- 
voltage discharge produces in mercury vapor not only atoms in the 
state 6 3 P 1 but also atoms in the metastable states 6 3 P and 6 3 P 2 , and 
because of their long lifetimes these metastable atoms attain relatively 
high concentrations. Therefore, the vapor shows particularly strong 
absorption for the lines starting from the metastable levels, and the 
fluorescence of the visible triplet 7 3 S, -» 6 3 P oh2 can be stimulated not 
only by absorption of the line 4358A, as before, but as well and even 



COMBINED ELECTRICAL AND OPTICAL EXCITATION 45 

more efficiently by absorption of the lines 4047 and 5416A. The relative 
intensities of the three components of the triplet do not depend on 
which of the three lines served for the secondary excitation : there is 
no evidence for the existence of a separate scattering process apart 
from fluorescence (441). (See Section 33 for further conclusions to be 
drawn from these experiments). Ga viola has shown that the relative 
intensities of the triplet components do not depend, either, on the 
relative concentrations of atoms in the various 6 3 P / -states. This was 
to be expected according to Bohr's theory, while an erroneous inter- 
pretation of wave mechanics led to a different conclusion.* 

The term systems of the rare gases are very similar to the system 
of mercury : they consist of singlet and triplet series. The true reso- 
nance lines are situated in the far u.v. and can be observed only with 
vacuum apparatus. However, the levels nearest to the ground state 
are metastable. In helium the lowest of these is the state 2 3 S lt which 
is the ground state for the orthohelium spectrum. Since intercombi- 
nation lines between the triplet and the singlet system of helium do 
not exist at all, the state 2 3 S 1 can become the ground level for genuine 
resonance radiation exactly as the normal ground state w 1 .?,, of an 
unexcited metal atom. Because of the high degree of their metastabi- 
lity the concentration of the metastable helium atoms can become 
rather high in an electric discharge (Figure 17). 

The resonance lines of orthohelium, as discovered by Paschen, 
form a doublet (instead of a triplet), because only two of the three 
2 s Pi-levels can be resolved. If helium of a few mm pressure is excited 
by a weak electric discharge, it absorbs the two infrared emission lines 
10830 and 10829A (2 3 P 2 «- 2 S S 1 and 2 3 P 1 +- 2 3 S 1 ) of a helium Geissler 
tube. The two lines are re-emitted by the absorbing gas without 
appreciable loss of energy, according to Paschen 's measurements. The 
state 2 1 S of parhelium is also metastable, but the atoms can be raised 
from this level to 2 1 P 1 or 3 1 P 1 by absorption of light and from there 
they can return directly to the ground state l^V Therefore, the con- 
centration of atoms in the state 2 1 5 remains relatively small in the 
electric discharge, and absorption of the line 20582A (2 1 P 1 -s- 2 1 S ) is 
rather weak ; it is even much weaker in emission because of the com- 
petition of the much more probable transition to l^S,, (the true 
resonance line of helium). The line 20582 A has never been observed 

* G. Hoffmann observed the absorption of the lines originating from, the 
levels 5 8 P t , in electrically excited vapors of cadmium and zinc and the 
absorption of the green line in electrically excited thallium vapor. However 
he made no mention of any fluorescence emission of these lines. 



46 



MONATOMIC GASES AND VAPORS 



in the fluorescence spectrum of electrically excited helium {1193). 
(The experimental conditions are particularly unfavorable for ob- 
servations of low intensities, since they cannot be made visually or 




ORTHOHELIUM PARAHELIUM 

Fig. 17. Grotrian diagram for He. 

photographically, but must be performed by means of thermopiles 
or bolometers). 

On the other hand, the second doublet of the main series of 
orthohelium at 3839A {3 3 Pj -> 2 s Si) has been obtained by McCurdy 



COMBINED ELECTRICAL AND OPTICAL EXCITATION 47 

in fluorescence, while the analogous line of parhelium at 501 5A was 
again missing. However, a number of orthohelium, lines were observed 
by Maxwell in a tube in which, as in Lees' and Skinner's experiment 
(see Section 18), helium was excited by a concentrated beam of elec- 
trons, while the spectral observations were restricted to the space 
outside of the path of the electrons. According to Maxwell, helium 
atoms which have been raised by electron collisions into the higher 
states of the parhelium term system leave the path of the electric 
discharge by diffusion and are then able to absorb and re-emit other 
lines of the parhelium spectrum (8 '76, 877, ggi ,gg2,ggs). [The reasons 
brought forward by Maurer and Wolf to disprove Maxwell's expla- 
nation of his experiments are far from being convincing {9go).] 

Lau and Reichenheim, also, admit the possibility of stepwise 
excitation in their experiments mentioned at the end of Section 16. 
In this case, the first stage of the process would not be due to an 
electron collision but to the absorption of the Lyman resonance line 
2P<- 15 of hydrogen. The short life of the 2P-atoms is supposed to be 
compensated by their high concentration? Ladenburg had shown 
much earlier, that the lines of the Balmer series are absorbed with 
high efficiency by electrically excited hydrogen {86g). 

However, stepwise excitation is, in general, important only when 
metastable states come into play as in the case of mercury and 
the rare gases. The system of the lower terms of neon is in all respects 
analogous to that of mercury, although the energy differences between 
the ground state and the lowest excited levels are much larger. Like 
mercury, neon has two genuine resonance lines corresponding to the 
transitions from the ground state 2 l 5 to 2 3 P lt 2 1 Pi (ls 4 ls 2 inPaschen's 
older notation). They are situated in the far u.v. and have, so far, 
been observed only under electric excitation. Two further 2P-levels, 
2 3 P and 2 3 P 2 (ls 3 and ls 5 , according to Paschen), are metastable, as 
in the case of mercury; neon atoms can be raised into these states 
from the ground state by electron collisions and comparatively large 
concentrations of such metastable atoms are present in equilibrium in 
an electric discharge through neon. If the total radiation of a neon- 
filled Geissler tube is focused into the space adjoining the path of 
the electric discharge in a neon glow lamp, this radiation excites a 
secondary fluorescence which is completely analogous to the secondary 
fluorescence of mercury, described previously. All those lines occur 
which are emitted from levels reached by absorption of atoms in the 
four P-stat.es and particularly in the metastable states. Line 6402A 
(3 3 Z) 3 -»■ 2 3 P 2 ) is of especially great intensity. This line is the genuine 



48 MONATOMIC GASES AND VAPORS 

resonance line of the metastable state 2 3 P 2 . In commercial neon glow 
lamps, the discharge proper is surrounded by a red luminescence ; De 
Groot explained it as a phenomenon of secondary fluorescence in the 
electrically excited gas. The stepwise-excited fluorescence of neon can 
be demonstrated even better in a "Hertz lamp." This is a tube filled 
with neon of low pressure and equipped with a hot filament cathode ; 
the electrons from the cathode are accelerated through a grid into a 
field-free observation chamber. If the accelerating voltage on the grid 
is large enough, the visible neon lines are stimulated by electron 
collision in the observation chamber. If the voltage is below 18 volts 
but larger than 1 6, the P-states alone are excited and red and orange 
lines appear as secondary fluorescence, if the Hertz lamp is irradiated 
with light from another neon discharge tube. If, under these con- 
ditions, the exciting radiation contains only the line 6402A, this 
resonance line is also the only one emitted in fluorescence (265,311, 
453,1008). If the grid voltage drops below 16 volts, fluorescence is 
produced neither by electron impact nor by optical excitation. 

By the same method, the emission of a great number of red and 
infrared argon lines and of some xenon lines was observed as secondary 
fluorescence in electrically excited argon and xenon, corresponding to 
transitions between terms analogous to those in neon (475,1008). 

C. The Absorption and Emission Process 

19. Absorption of Primary Radiation. Resonance radiation has 
been discovered by Wood in the vapors of mercury and sodium, and 
the phenomenon has been investigated in these two vapors more 
thoroughly than in any other vapors or gases. This is due rather to 
the fact that adequate light sources were available, than to the rela- 
tively high vapor pressures of the metals at low temperatures. The 
vapor pressures needed for the excitation of resonance radiation are so 
low that they can be obtained for many other metals without great 
difficulties. Mercury resonance radiation is already very strong at 0° C 
(p = 1.9- 10 -4 mm) and can be observed down to temperatures of 
— 50° C (j> < 10~ 6 mm). In sodium vapor all measurements can easily 
be performed visually at 100° C (p > — ' 10~ 7 mm) if a suitable source of 
primary light is used. Since low vapor pressure is essential for ob- 
taining pure experimental conditions, the absorption lines of the vapor 
are exceedingly narrow and only the central parts of the lines emitted 
by the primary light sources contribute to the excitation. If great 



ABSORPTION OF PRIMARY RADIATION 49 

amounts of sodium chloride are injected into a Bunsen flame, its 
yellow radiation becomes much brighter without increasing the in- 
tensity of the resonance radiation which it excites in sodium vapor. 
It is well known that higher sodium concentration in the flame 
increases only the width of the D-lines, but not the intensity in the 
center of the lines (1860,1866). 

[The occurrence of the D-lines in the light of the night sky is 
greatly enhanced during a short period immediately after sunset and 
before sunrise and has been interpreted by Bernard, Bricard and 
Kastler, and others as resonance radiation excited by sunlight in a 
layer of sodium vapor- at an altitude of about 75 km. Because of the 
improbability of the presence of free atomic sodium in the high 
atmosphere, others ascribed the phenomenon to the photodissociation 
of NaCl into CI + Na (3 2 P) with subsequent emission of the atomic 
sodium lines (see Sect. 70). An argument in favor of the first hypo- 
thesis is seen in the sharpness of the lines : their width is, according 
to their absorbability is sodium vapor, far less than 0.03A and corre- 
sponds to the Doppler effect at 240° K. If produced by photodissoci- 
ation of sodium chloride the lines would have an appreciably greater 
width, because some of the molecules would absorb light quanta of an 
energy exceeding the heat of dissociation of NaCl. This argument is not 
quite convincing, however, because the energy distribution in the 
spectrum of the sun must slope very steeply at the wavelength of 
1 700A which is needed for the dissociation process, so that light of still 
smaller wavelengths would contribute very little to the reaction. An 
unequivocal solution of the problem would be provided by a determi- 
nation of the altitude at which the phenomenon takes place : light of 
wavelengths equal to, or smaller than, 1 700A cannot penetrate to an 
altitude below 100 km. On the other hand, it may be possible to 
explain the existence of atomic sodium in the atmosphere at an altitude 
of 75 km by the presence of atomic oxygen, which would automatically 
maintain a certain concentration of sodium atoms by the continuous 
reaction (g4,i6y,ig^,ig6,20$,2i6,26g,42j,y3oa,'j3ob,iy6g) : 

Na + O -> NaO; NaO + O -> O s + Na; Na + O -+ NaO . . .] 

When, in his earliest experiments, Wood used a commercial 
high-pressure mercury lamp, resonance radiation was excited in 
mercury vapor only during the first few seconds after striking of the 
arc. With rising temperature of the lamp its radiation, including the 
line 2537A, became stronger, but the intensity at the center of this 



50 MONATOMIC GASES AND VAPORS 

line decreased and dropped, because of self-reversal, eventually to 
zero (1866). 

At very low vapor pressures in the resonance tube, the absorption of 
the primary radiation is small and the resonance emission can, there- 
fore, be observed over a relatively long path of the exciting beam. 
Since the secondary absorption of the resonance radiation in the vapor 
is insignificant, a sharply delimited beam of light is produced, with 
slowly diminishing intensity along its path ("beam fluorescence"). 
The intensity of the mercury resonance decreases to about 50 % after 
the exciting ray has passed through 0.5 cm of mercury vapor at room 
temperature {p ~ 10 -3 mm). From these data, Wood derived an 
approximate absorption coefficient of the exciting radiation, but he 
himself pointed out that the absorption does not follow a strictly 
exponential law. According to Goos and Meyer, the apparent "ab- 
sorption coefficient k" determined by this method decreases con- 
tinuously with increasing distance d from the entrance window. From 
one of their photographs, for instance, k was calculated to be 1.8, 1.5, 
and 1 .2 cm -1 for distances <? = 3, 6, and 9 cm respectively. The dif- 
ferent parts of the exciting line are not equally absorbed in the vapor, 
the absorption being much stronger for the center of the line than for 
the outer parts. The width of, and the intensity distribution in, the 
exciting line are of decisive importance for its absorbability (520, 
1023,1654,1867). 

If the vapor pressure in the resonance tube is increased, the ab- 
sorption of the primary and of the secondary radiation becomes 
stronger. Therefore, the resonance intensity along the exciting beam 
decreases more rapidly and, at the same time, the luminosity becomes 
more and more diffuse, until it fills the whole volume of the tube 
(volume fluorescence). Eventually the phenomenon is concentrated 
within a narrow layer adjoining the entrance window; the "volume 
fluorescence" is transformed into "surface fluorescence." This state is 
reached in saturated sodium vapor at about 300° C and in mercury 
vapor somewhat below 100° C (322,1874). 

If the fluorescence of thallium is excited by .lines which are 
absorbed by atoms in the ground state 6 2 P 1/2 (for instance, the line 
3776A), surface fluorescence is observed exclusively in vapor saturated 
at 900° C (p '--' 1 mm), while the green thallium line is still able to 
produce fluorescence well inside of the tube; under these conditions, 
only about one per cent of the atoms are in the state 6 2 P 3/2 and are 
thus able to absorb the green line. 

In volume and surface fluorescence, the main part of the radiation 



FLUORESCENCE YIELD AND WIDTH OF RESONANCE LINES 51 

leaving the tube is not emitted by atoms which have been directly 
excited. In general, the absorbed energy is transferred several times 
from one atom to another before it leaves the fluorescing gas. This 
energy transfer is due not only to reabsorption and re-emission, but 
also to so-called collisions of the second kind, which will be dealt with 
in a later chapter. 

20. Fluorescence Yield and Width of Resonance Lines. The yield or 
efficiency of resonance radiation is the ratio of the energy emitted by 
a given volume to the energy absorbed in the same volume. In the 
absence of all perturbations, the whole energy taken up by an atom 
can be re-emitted only in the form of radiation; hence, the efficiency 
0=1 is to be expected. The experimental results, which were ob- 
tained with resonance radiation of different gases and vapors, have 
confirmed this expectation. Paschen's measurements on the infrared 
orthohelium lines are probably the most accurate. He determined at 
first, by means of a thermopile, the intensity emitted by his helium 
resonance lamp in a certain solid angle ; then he focused an image of 
the resonance lamp, by means of a spherical mirror of known aperture 
into the lamp itself, thus increasing the intensity of its radiation, and 
repeated the measurement with the thermopile. Finally, he deter- 
mined the absorption coefficient of the resonance lamp for its own 
radiation. The total yield was thus found to be 95 % {1193). The same 
method was used by Gerlach for the resonance radiation of mercury, 
employing a- photoelectric cell instead of a thermopile. The yield was 
of the order of 100 % in this case also, although the precision was less 
than in Paschen's experiment, since the reflection coefficient of the 
mirror for the line 2573A was not exactly known. The same result had 
already been obtained by Wood in a more qualitative way. Finally, 
Dunoyer and Wood proved by a very simple and convincing method 
that sodium vapor re-emits absorbed light energy completely as 
resonance radiation. If surface fluorescence is excited in sodium vapor 
at 300° C by the radiation from a sodium resonance lamp, the luminous 
layer has the same brightness as an adjoining perfectly white surface. 
If the exciting resonance lamp is replaced by a sodium chloride flame 
which emits D-lines of much greater width, the white area appears far 
brighter than the surface fluorescence {324,1874,1881). [A criticism 
by Vavilov which was brought forward against this conclusion does 
not seem to be justified (compare chapter IV, Section 123).] 

The width of the resonance lines is determined mainly by the 
temperature of the vapor or rather by the Doppler effect resulting 
from the thermal agitation, as long as the excited atoms are not 



52 MONATOMIC GASES AND VAPORS 

appreciably perturbed by interaction with other atoms or molecules. 
If, as in most experiments, the resonance emission is observed in a 
direction perpendicular to the exciting beam, the width and inten- 
sity distribution of the line in the primary light have no influence : each 
atom absorbs radiation only of the frequency which, in a system moving 
with the atom, coincides with the center of the line. On the other 
hand, the line width, as seen by a stationary observer, is determined 
exclusively by the Maxwell velocity distribution of the excited atoms 
with respect to the observer. Rump has shown that the width of the 
mercury resonance line increases according to theoretical prediction 
if the temperature of the vapor is altered, while the density in the 
resonance tube and the intensity of the primary radiation are kept 
constant. In these experiments the source of primary radiation was 
another resonance lamp and the relative values of the line width were 
obtained by measuring the absorption of the resonance radiation in a 
cell filled with mercury vapor of constant temperature and pressure. 
However, the width of the resonance line leaving the resonance tube 
does not, in general, correspond exactly to the width of the absorption 
line as postulated by theory ; even under the most favorable conditions 
a slight re-absorption of the central parts of the line cannot be avoided. 
The intensity distribution of the line resembles very closely a Gaussian 
distribution, but the greater the density and the depth of the re- 
absorbing layer, the more the apparent width of the line exceeds the 
true Doppler width (1394,1928). 

If the resonance radiation is observed in a direction parallel to 
the direction of the primary radiation, the intensity distribution in the 
resonance line is closely related to the intensity distribution in the 
exciting line ; if the exciting line is self -reversed, the fluorescence line 
is also reversed. Under these conditions, the intensity of the resonance 
radiation is less diminished by absorption in a layer of mercury vapor 
when it is observed in the direction of the primary beam than when 
it is observed in a perpendicular direction (1055). 

If the line width is essentially determined by some sort of pertur- 
bations and not by the Doppler effect, the intensity distribution in the 
resonance line is independent of the exact wavelength and of the 
energy distribution of the exciting line, as long as the wavelength 
of the exciting line coincides with a part of the broadened absorption 
line, and as long as the perturbations at the moment of absorption 
and at the moment of emission are independent of each other. If an 
atom, is perturbed by interaction with another molecule and, therefore, 
preferentially absorbs light of a frequency different from the resonance 



FLUORESCENCE YIELD AND WIDTH OF RESONANCE LINES 53 

frequency, it emits afterwards light corresponding to the center of 
the resonance line if it has left the sphere of the perturbation before the 
emission sets in. The angle formed by the direction of observation and 
the direction of the exciting beam is, in this case, of no importance for 
the "restoring" of the normal intensity distribution in the resonance 
line. The validity of these conclusions has been proved experimentally 
for the mercury resonance line, which was broadened by the addition 
of an inert gas {1183). 

This "restoring" of the normal intensity distribution in the line 
may be considered as the distinctive feature of resonance radiation as 
compared with Rayleigh scattering-notwithstanding the continuous 
transition between the two phenomena. If the frequency v of the 
primary radiation does not coincide with the characteristic frequency 
v of the unperturbed atom at rest the "virtual oscillators" of all 
atoms perform forced oscillations of relatively small amplitudes and 
thereby scatter the impinging radiation with low intensity and un- 
changed frequency. If v is within the Doppler width or within the 
width of the absorption line caused by a perturbation, the charac- 
teristic frequency of comparatively few atoms having high velocities 
or being strongly perturbed will coincide with v and they will be 
excited to vibrate with large amplitudes. The resonance radiation 
emitted by these atoms will be much stronger than the light of frequen- 
cy v scattered by the other atoms. The Rayleigh scattering prevails 
only in those parts of the spectrum where the absorption caused by 
Dopplef-broadening or collision-broadening of the resonance line 
practically vanishes. (Compare Section 82). 

The half-width of the D-lines in the resonance radiation of sodium 
vapor at 300° C has been determined by Dunoyer and Wood and by 
Strutt, both using interferometric methods. The value of 0.02A which 
they obtained is in good agreement with the value computed for the 
Doppler width at 600° K under the assumption that the line would 
be infinitely narrow at absolute zero. Under the prevailing conditions, 
the line width was exclusively determined by the thermal Doppler 
effect and not by radiation-damping nor by external perturbations 
{324,1591). 

The Doppler width becomes almost negligible if an atomic beam 
of the vapor is excited by a light beam perpendicular to the atomic 
beam and if the fluorescence is observed in a direction perpendicular 
to either. By using suitable diaphragms for the limitation of the 
atomic ray, the thermal agitation of the atoms in the directions 
perpendicular to the ray can be reduced to a value corresponding to 



54 



MONATOMIC GASES AND VAPORS 



a few degrees K {30J). If the mercury resonance line is excited under 
these conditions, its width is of the order of 10~ 5 A and is probably 
caused by radiation-damping alone ; 93.5 % of its intensity is absorbed 
in a layer of 5 mm thickness of mercury vapor saturated at 20° C 
(p = 1.3-10- 3 mm) (1919). 

21. Hyperfine Structure. The hyperfine-structure components of 
the D-lines are separated from each other by distances not exceeding 
0.01A. If the temperature of the vapor is sufficiently high for the 



100 




16 x 10 s 



H in gauss 



Fig. 18. Magnetic resolution of the hyperfine struc- 
ture of the Hg-resonance line by the Schein method 
(Buhl), I = transmitted energy. 



observation of resonance radiation, the hyperfine structure of the lines 
is hidden, under normal conditions, by the Doppler width of the lines. 
However, if the resonance radiation is excited in an atomic beam, the 
hyperfine structure can be resolved (J07). 

The Doppler width of the mercury resonance line is smaller 
owing to the greater atomic weight of Hg and, furthermore, the vapor 
pressure becomes greater at lower temperatures than in sodium vapor. 
Therefore, spectrograph^ methods of sufficient resolving power show 
the hyperfine structure of the mercury resonance line 2537A in a tube 
containing the vapor at room temperature. Malinowski was the first 
to prove that the line consists of more than one component. In his 
experiments, radiation emitted by a mercury resonance lamp passed 



HYPERFINE STRUCTURE 



55 



through an absorption tube which contained mercury vapor and which 
was placed between the pole pieces of an electromagnet. Stepwise 
increase of the magnetic field shifted the Zeeman components of the 
absorption line. Measuring the absorption of the unshifted resonance 
line in the absorption cell for every field strength, Malinowski obtained 
several maxima and minima of transmitted energy and concluded 
that the line consisted of two or more components with a width of 
about 2.3-10 _4 A and a mutual distance of 3-lCr- 3 A {972). Later, 
Wood succeeded in analyzing completely the line emitted by an 
electric discharge in mercury vapor; he used two crossed Lummer- 



RED 


29 


.27 










VIOLET 








2377 






19.17 














a 

A 

/ 
20« 


6. 84 
5.48 
6.85 


X Z0Z 




X 
200 




14. < 

4.56 

A 1 

1 


>5 

9.89 

*I98 


(3.24 
C T 2.28 

T 

8 1 10.96 

1 

1 



-333 


-178 





+ 132 +167 


+ 21.5 


+ 11.5 





- 10.4 


I 


I 


11 


17 



+ 394 -lO^cm"' 
-25.4 -I0" 3 A 



Fig. 19. Hyperfine structure of the Hg-resonance line 
(Schueler and Keyston). 



Gehrke quartz plates and found five approximately equidistant com- 
ponents of equal width (i8go). 

Several investigators confirmed Wood's results concerning the 
structure of the line also when the radiation was excited by resonance. 
Schein came to the same conclusion by improving Malinowski's 
method, and Buhl improved it even further by using, as primary 
radiation, a single hyperfine-structure component which was isolated 
by a "Mrozowski filter" (Section 9). Figure 18 shows the intensity 
transmitted through the resonance lamp as a function of the applied 
magnetic field (185,645,1078,1420-1422). 

The complete hyperfine-structure scheme of the mercury line 
2537A is reproduced in Figure 19, in which the distances from the 
central component are plotted as abscissas, theunits being thousandths 
of an Angstrom. The existence of hyperfine structure is due to two 
causes. The energy levels of the seven mercury isotopes, which are 
listed in Table 5 according to Schueler and Keyston, have slightly 



56 



MONATOMIC GASES AND VAPORS 



Table 5 
The Isotopes of Mercury 



Atomic 
weight 


Relative 
amount in % 


Nuclear 
spin * 


Atomic 
weight 


Relative 
amount in % 


Nuclear 
spin « 


204 
202 


6.85 

29.28 

23.27 

9.89 

0.10 









201 
199 


13.67 
16.45 


3/2 
1/2 


200 
198 
196 


30.12 






69.39 





different energies. Furthermore, the terms of the mercury isotopes 
of odd atomic weight ("odd isotopes"), consist of 2i + 1 or 2/ + 1 



CJ 



-7% 



-6 3 /0 



■e*P, 



196 (0.10%) 
Similarly 
198 (9.89%) 
200 (23.77%) 
202 (2937%) 
204 (6.65%) 

J -6 ! 5„ 




f 7 ! 









6% 



'\ 



Ji 



6*. 



201 (13.67%) 



,JL 



Fig. 20. Hyperfine-structure levels of the lower electronic states 
of Hg [Boggs and Webb (126)] 

sublevels (compare Section 13). The hyperfine-structure terms of the 
lower levels of the mercury isotopes are represented in the diagram of 
Figure 20. The term schemes for the five even isotopes are similar, 
but the absolute heights of the levels differ. Some of the energy 
differences, however, are so small that the corresponding lines cannot 
be separated even with instruments of highest resolving power. In 
Fig. 19, components of line 253 7 A which belong to even isotopes 
are designated by the symbols X 20i , X W2 , etc., those belonging to 
Hg 201 by a, b, c, and those belonging to Hg 199 by A and B. Lengths of 
the lines in thediagram correspond to the intensitiesof the components. 
The diagram shows, furthermore, why the line was resolved into only 



HYPEEFINE STRUCTURE 57 

five components by Wood and other investigators. All details con- 
cerning the width and the intensity distribution of the lines apply 
without alteration to the individual components of the hyperfine 
structure. 

Mrozowski succeeded in exciting some of the hyperfine-structure 
components of the line 2537 separately by resonance, using the "filter 
method" described in Section 9. According to the magnetic field 
strength and the orientation of the polarizers, he obtained practically 
only the component — 25.4,* or the components — 10.4 and + 21.5, 
or the components and + 11.5. The various components which have 
unequal intensities in the emission spectrum also have different ab- 
sorption coefficients in mercury vapor of constant density. (This is a 
further reason for the nonexistence of a homogeneous absorption 
coefficient of the resonance radiation in mercury vapor). The relative 
intensities of the hyperfine-structure components vary in a resonance 
lamp, along the beam of the primary light, since at sufficiently low 
vapor pressures (so that collisions during the life of the excited states 
are excluded) every component is emitted only insofar as it is directly 
excited by absorption {ioji). 

Figure 20 shows, furthermore, that the hyperfine structure of the 
triplet lines 7 3 S X ^ 6 3 P 7 (J = 0, 1,2,: 5461 A, etc.) which can be ex- 
cited by stepwise absorption is much more complicated. The relative 
excitation probabilities are now different for all components in each 
of the two stages (6 3 P 1 ^- S^q and 7 3 S 1 «- 6 3 P X ), and thus the relative 
intensities of the hyperfine-structure components can differ widely in 
the exciting and in the fluorescence radiation (126). The weaker com- 
ponents, in particular, are apt to be practically missing in the fluo- 
rescence spectrum because they are little absorbed in the resonance 
lamp. If the radiation from a mercury lamp passes through a tube 
containing a mixture of Hg- vapor and N 2 in which metastable mercury 
atoms are produced at a high concentration by irradiation with the 
resonance line, the absorption of the lines 4047 and 2752A, both 
originating from the state 6 3 P , does not obey an exponential law with 
increasing length of the absorbing layer because of the unequal ab- 
sorbability of the various hyperfine-structure components of these 
lines (five components in the case of 4047, two in the case of 2752) 
{23ia,i2 54,125s). 

Terenin was the first to mention these relations. Later, Boggs and 

* According to Ellett it is impossible to isolate completely this component 
by the Mrozowski method; the filter always transmits simultaneously the 
component + 21.5 with about the same intensity. 



58 MONATOMIC GASES AND VAPORS 

Webb computed the relative intensities of all hyperfine-structure 
components of the lines 5461, 4358, and 404 7A under the assumption 
of stepwise excitation and they obtained excellent agreement with the 
experimental results. They supposed the intensity distribution in the 
primary radiation to be completely free from self-reversal and the 
primary radiation to be completely absorbed in the fluorescing vapor 
(126). 

Apart from the extensive observations on mercury vapor, the 
only investigation of the hyperfine structure of a line excited by 
resonance dealt with the zinc line 3076A. It was not possible to resolve 
the individual components of the line by means of the Malinowski- 
Scheibe method ; however, the line width was found to be about twice 
as large as the Doppler width of a single line. Billeter assumed that 
the components belonging to the three even isotopes (Zn 64 , Zn 66 , and 
Zn 68 ) overlap, because the distance of the outer components from the 
central line does not exceed 1.75- 10 -3 A. The relative abundance of the 
only odd component is not more than 4 % and, therefore, it can practi- 
cally be neglected so far as its contribution to the resonance radiation 
is concerned (33,110-112). 

22. Experimental Determination of Lifetime t. The mean lifetime t 
of the excited state of an atom has been defined in the Introduction as 
the time during which the intensity of its radiation decreases from I 
to l/e-I . J is the intensity at the moment when the excitation process 
is ended, t can be computed from the natural width of the line 
("radiation-damping") or from the absolute intensity of the line in the 
absorption spectrum ("oscillator strength"), using the theory of 
dispersion. These calculations are based essentially on absorption 
measurements, even if resonance lamps are used for the production of 
radiation, and, therefore, are not to be dicussed here.* Some of the 
values obtained in this way are given for comparison in Table 1 1 . 

Since the lifetime of a resonance line in the visible part of the 
spectrum may be expected to be of the order of 10 -8 sec, it is obvious 
that no afterglow could be observed in optically excited sodium or 
mercury vapor by any of the earlier methods. Not only did the 
mechanical phosphoroscopes fail, but Dunoyer was also unable to 
observe a shift of the luminescent spot in an atomic beam of sodium, 
in which resonance radiation was excited by irradiation (Figure 21) 
(3 2 3)- The average atomic velocities at the temperature which he used 

* For a full discussion of these and other methods, the reader may be 
referred to Mitchell and Zemansky's Resonance Radiation and Excited Atoms, 
chapter III. 



EXPERIMENTAL DETERMINATION OF LIFETIME T 



59 




OVEN 



Fig. 21. Excitation of resonance radi- 
ation in an atomic beam( Dunoyer). 



are of the order of 10 4 or 10 5 cm per sec, and since a displacement of 
the upper edge of the luminous spot by less than 10 -2 cm could not be. 
detected, his experiment proved that lO -6 sec was the upper limit of t 
The lifetime of the very "improbable" intercombination resonance 
line of cadmium (3261 A, S^-*- d^) is larger than this value; it was 
actually possible to obtain the lifetime t = 2.5- 10~ 6 sec for this line by 
means of Dunoyer's method, 
while the singlet resonance line 
of cadmium (2288A, 5 1 P 1 ^5 1 S ) 
is far too short-lived for an ex- 
periment of this kind. The life- 
time of the intercombination 
line of zinc (3076A, 4 3 P 1 -*4 1 S ) 
is considerably longer (compare 
Section 14) but its transition 
probability is very low and the 
efficiency of resonance excitation 
is so small that the failure to 
detect an afterglow in an atomic 
ray of zinc vapor is easily ex- 
plained (I532J533)- 

The mean life of the metastable state 6 3 P into which mercury 
atoms are transferred by the absorption of the resonance line and a 
subsequent collision with a nitrogen molecule is so long that it is 
accessible to measurements with a Becquerel phosphoroscope. It is 
possible to determine the period during which the visible triplet 
7 3 5 1 H>6 3 P 012 can be excited "stepwise" in the vapor after the 
irradiation with light of wavelength 2537A has been interrupted. 
Furthermore, the line 253 7 A itself shows a measurable afterglow 
originating from atoms which are raised from the metastable state to 
the level 6 3 P 1 by a renewed collision with a nitrogen molecule (27,28, 
1252,1253). The values of t determined in this way are of the order of 
magnitude of 10~ 3 to 10 -2 sec; however, they do not correspond to 
the genuine "natural lifetime" of the metastable state, but only to its 
lifetime under the specific experimental conditions, such as quenching 
collisions, diffusion to the walls, etc. The true life of the state 6 3 P of 
the even mercury isotopes in the absence of all perturbations would be 
infinite. Mrozowski proved by observation of its hyperfine structure 
that the emission of the "forbidden line" 2656A (6 3 P ^ S^) occurs 
exclusively in the odd mercury isotopes. For these, the strict selection 
rule mentioned in Section 13 is invalidated so some extent by the 



60 MONATOMIC GASES AND VAPORS 

influence of the nuclear spin, so that the natural lifetime of their 
metastable state is of the order of magnitude of one second. Con- 
sidering the great effective cross section of energy transfer between 
excited states of nearly equal energy (see Section 35), the energy stored 
in the 6 3 P -atoms of the even mercury atoms has a hundred percent 
probability of being transferred to an odd isotope even at low vapor 
densities and thus the lifetime of all mercury isotopes in the 6 3 P -state 
is only of the same order of magnitude as that of the odd isotopes 
(1071,1081). 

Experiments on the lifetimes of metastable states of other 
elements yielded similar results, but since these experiments consisted 
in absorption measurements in electrically excited gases, they are 
beyond the scope of this book. 

The equation for the relation between fluorescence yield and life- 
time (Section 4) was derived by Stern and Volmer originally with the 
purpose of determining the lifetimes of excited states. In order to 
obtain quantitative results, they assumed that every "gas-kinetic 
collision" between an excited and a quenching molecule* is a 
"quenching collision." It was shown later that this assumption is not 
correct in general, and, therefore, the principle is better adapted for 
finding the "effective quenching cross sections" of molecules if the 
values of t have been determined by other measurements (1275,1571). 

The measurement of the degree of polarization of resonance 
radiation in magnetic fields provides a method which has been applied 
most frequently and successfully for the determination of the lifetimes 
of excited atoms in fluorescent vapors ; this method is treated in Part 
E of this chapter. As far as the fluorescence of monatomic vapors is 
concerned, fluorometers have been used only in the case of the D-lines 
of sodium, for which Hupfeld obtained a lifetime t = 1.5- 10 -8 sec, 
while Duschinsky found by the same method the appreciably smaller 
value of t = 0.8- 10~ 8 sec. Duschinsky performed his experiments at a 
vapor pressure of 2- 10" 6 mm (saturated at 135° C); he assumed that 
at the higher vapor pressure of 8- 10~ 5 mm (saturned at 190° C) which 
subsisted in Hupfeld's experiments the resonance radiation was partial- 
ly "imprisoned," thus increasing the apparent duration of the emission 
process. Such an effect must actually occur, as will be discussed in the 
next section, but it is doubtful whether it can be made responsi- 
ble for the discrepancy between the two measuremenss. All other 
methods by which the lifetime of the 3P-states of sodium can be 

* a, in Equations (5)-(7), section 4, is in this special case the probability of 
quenching, i.e., the number of quenching collisions per second. 



IMPRISONED-RADIATION RECOIL OF EXITED ATOMS 61 

determined, produce values of t which are in much better agreement 
with Hupfeld's than with Duschinsky's results (326,642). 

Gaviola, and in more detail Weisskopf and Duschinsky, have 
discussed the question whether the results obtained by means of a 
fluorometer correspond to the real lifetimes of the excited states in 
resonance radiation; they all come to the conclusion that, under the 
prevailing experimental conditions, the method can be applied {327, 

328,1813,1815). 

23. "Imprisoned Radiation". Recoil of Excited Atoms. K. T. 

Compton, H. W. Webb, and at greater length E. A. Milne, have 
treated the problem of a radiation which is "imprisoned" in a volume 
of vapor because of multiple reabsorption and re-emission processes. 
It is a typical diffusionproblem(2j2,^57,590,765,766,ro3oa). The result 
of the mathematical treatment is that when the number N of atoms 
per unit cross section between the entrance window for the exciting 
radiation and the exit window for the fluorescence radiation is in- 
creased, the apparent lifetime also increases. N is proportional to the 
vapor pressure p and thickness d of the layer of vapor and, under 
the simplest assumptions, the apparent value of t is directly pro- 
portional to N. The theory has been tested by Hayner and by Zemanski 
for the mercury resonance line and has been corroborated, at least in 
a qualitative way, by the latter.* In his experiments the mercury 
vapor, saturated at different temperatures (60 to 130°C), was contained 
in plane parallel quartz cells 1.3 and 1.95 cm thick; the cells were 
placed between the rotating discs of a phosphoroscope, and values of r 
were obtained which were of the same order of magnitude as those 
calculated according to Milne's theory. However, a comparison of the 
figures collected in Table 6 shows that increasing p or d does not have 
the same influence on the value of t. Above a certain pressure, t 
even drops again : collisions of excited atoms with other mercury atoms 
are able to quench the fluorescence. There are other reasons why 
the use of the mercury line 2537A makes the results of these obser- 
vations rather ambiguous ; as a matter of fact, the observed times of 
the afterglow may be caused by a number of complications quite 
unrelated to the ' 'imprisonment" of radiation, for instance, the transfer 
of excited atoms into the metastable state 6 3 P , or the formation of 
Hg 2 -Molecules and the subsequent emission of the resonance line 

* According to measurements by Webb and Messenger on electrically 
excited mercury vapor, the time during which the resonance radiation is im- 
prisoned in the vapor becomes about ten times longer if the vapor pressure is 
increased from 10" 4 to 10~ 3 mm. [Phys. Rev., 33, 319 (1929)]. 



62 



MONATOMIC GASES AND VAPORS 



following the dissociation of these molecules. These phenomena will 
be dealt with in a later section (206,590,1923). 

Zehden confirms that the phenomenon of imprisoned radiation 
also begins to be noticeable in saturated sodium vapor above 170° C, 
but quantitative measufements are not available for this case [192 1). 

It has been suggested that the center of a resonance line should 
be displaced appreciably by the effect of many repeated processes of 
reabsorption and re-emission (Compton effect of optical radiation). An 
individual scattering process would produce a change in wavelength of 
the order of only 10~ 7 A, but the cumulative effect of a great number of 
such processes was supposed to produce a measurable change in the 
wavelength of a resonance radiation which had been imprisoned in a 

Table 6 
The Time of Afterglow t of Imprisoned Mercury Resonance 
Radiation as a Function of Vapor Pressure p and of Thickness 

of Vapor d 







d = 1.30 cm 


d = 1.95 cm 


T co 


p (mm) 












2V-10-" 


T-10 1 


JV-10-" 


T-10« 


60 


0.026 


— 





1.50 


0.376 


70 


0.050 


1.82 


0.356 


2.73 


0.704 


80 


0.092 


3.25 


0.518 


4.88 


1.13 


90 


0.163 


5.72 


0.827 


8.59 


1.41 


100 


0.279 


9.44 


1.06 


14.2 


1.45 


110 


0.466 


15.3 


1.11 


23.0 


1.30 


120 


0.756 


24.4 


0.944 


36.7 


1.04 


130 


1.197 


37.9 


0.74 


56.6 


0.76 



volume of vapor. It can easily be proved, however, that as long as the 
width of the line is determined by the Doppler effect or by collision- 
damping and not by radiation-damping (and this is the case for all 
experiments under discussion), a phenomenon of this type cannot 
occur, because on the avefage the successive Compton effects will not 
add up, but will compensate each other (413, 1032, 1181b, 118 5, 1753). 
Fritsch has shown experimentally that actually every absorption 
and emission process causes a recoil of the atom and, therefore, must 
also produce a Compton effect. He excited the resonance radiation in 
a narrowly denned atomic beam of sodium vapor by a light beam 
perpendicular to it, as in Dunoyer's older experiment (Figure 21). The 
atomic ray broadens symmetrically in the plane which is perpendicular 
to the direction of the exciting radiation, because the emission processes 
occur with equal probability in all directions within this plane. In the 



POLARIZATION OF RESONANCE RADIATION IN MAGNETIC FIELDS 63 

direction of the exciting radiation, however, an unsymmetrical shift 
of the atomic beam is superimposed upon this broadening, because 
the absorption processes take place only from one side. The effects are 
very minute; they were rendered visible by the displacement of the 
spot where the atomic beam impinged on the receiving instrument, 
20 cm distant from the point of excitation, using the exceedingly 
sensitive methods which have been developed for the investigation of 
molecular beams (440). 

D. Polarization of Resonance Radiation 
in Magnetic Fields 

24. Classical and Quantum- Mechanical Interpretation. The ex- 
istence of a partial polarization of the resonance radiation which is 
excited by plane-polarized light has been the subject of some con- 
troversy. Eventually, Wood and Ellett found that it depended to a 
large extent on the presence of external magnetic fields which may 
be very weak and quite accidental, as well as on the direction of obser- 
vation and, finally, on the nature of the individual resonance lines 
(351,1344,1888,1896). 

The vibrations of the electrical oscillators of the Lorentz theory 
must always follow the direction of the electric vector E of the exciting 
radiation, and thus the resonance light emitted by the oscillator must 
be polarized in the same direction as the primary radiation. This holds 
for any azimuth under which the fluorescence is observed. On the 
other hand, the intensity of the fluorescence is a function of the angle 
of the azimuth ; it has its maximum in the direction perpendicular to 
E and tends, theoretically, towards for the direction parallel to E. 

Even excitation with unpolarized light should produce the 
emission of totally polarized fluorescence in the direction exactly 
perpendicular to the primary beam. In this case, the degree of 
polarization drops to zero if the fluorescence is observed in the direction 
of the exciting ray, while simultaneously its intensity becomes twice 
as large. 

The absorption and emission of light by an anisotropic oscillator 
having the same frequency in all directions could not be treated by 
means of the classical theory without the introduction of rather 
artificial assumptions (compare Section 118). 

The quantum theory in its original form was able to solve the 
problem of the polarization of resonance radiation only for atoms 



64 MONATOMIC GASES AND VAPORS 

which are subjected to the action of an external directional force, for 
instance, a magnetic field. In the absence of such fields the atoms are 
degenerate with respect to the quantum numbers which determine 
their orientation in space. 

Hanle was the first to publish a short note in which he showed 
that Wood's and Ellet's striking observations could be interpreted in 
principle as caused by Zeeman effects in the absorption and emission 
processes. Making use only of the classical Lorentz model, he could 
not explain why the behavior of the mercury resonance line and of the 
D-lines differed so widely (5JO,$ji). Some time later, several investi- 
gators were able almost simultaneously, to give a complete interpre- 
tation of the experimental observations by means of quantum theory* 
i 1 59,348,351, 695,1142, 1180,1282, 1339). However, they made the as- 
sumption that the spectral terms split in the magnetic field according 
to the inner quantum number J, without taking into account the 
influence of the hyperfine structure. While this supposition yields, in 
general, correct results for the even isotopes, important discrepancies 
occur for odd isotopes, if the magnetic fields are not strong enough to 
produce a Paschen-Back effect of the hyperfine structure. In the 
following sections, this condition is supposed to be realized. However, 
many experiments have been executed with weak or even vanishing 
magnetic field strength; hence, the results sometimes seemed to 
disagree with the theory. These cases are dealt with in Part E (576). 

25. The Mercury Line 2537A as Most Simple Example. Corre- 
sponding to the classical model, the ideal case would be a line showing 
the "normal Zeeman effect," a line of the type 1 P 1 -+ 1 5 , for instance, 
the singlet resonance line of mercury (1849A). A line of this class has 
not yet been thoroughly investigated. No observations dealing with 
the polarization of the mercury line are available, and the publications 
on the corresponding lines of cadmium and zinc are far from being 
complete. However, for all questions to be considered heie, the type 
represented by the mercury line 2537A is practically equivalent. The 
Zeeman triplet of this line in a strong magnetic field differs from the 
Lorentz triplet only by the "splitting factor" g = 3 / 2 : the distances 
A v between the outer components and the undisplaced line are 3 / 2 of 
those in the normal triplet for which A v = 4.7-10 _5 c-H (c is the 
velocity of light in vacuo and H the magnetic field strength in gauss). 
If a line of this type is excited by resonance in a magnetic field, 

* As a matter of fact, a large part of this explanation was already contained 
in an earlier paper by Foot, Ruark, and Urey, but without applying it to Wood's 
and Elle'tt's experiments (406). 



THE MERCURY LINE 253 7A 65 

its behavior can be visualized easily by the assumption that each 
atom carries three oscillators of equal frequency : a linear oscillator e, 
vibrating parallel to H, and two rotors r x and r 2 , rotating in opposite 
directions, with their plane of rotation perpendicular toH. In Figure 22, 
E is the electric vector of the exciting light and H the vector of the 
magnetic field. The direction of the primary radiation is supposed to 
be parallel to the X-axis. The figure shows, for certain orientations of 
E and H (case I and case II), how only e or only the rotors r are 
excited, and how, in consequence, 



H 

ij M H 

* e r i r , 



IH 



the resonance radiation should be 
completely plane polarized if the 
direction of observation is parallel 
to the Y-axis. Wood's and Ellett's 
measurements yielded for the 
degree of polarization p of the / e 

mercury resonance line the values Y 

p = 90 % in case I and^> = 60 % Fig. 22. Orientation of electric oscil- 
incase II. Keussler obtained 80% lators in a magnetic field H. 
in case I and 67 % in case II. The Y ■= direction of observation, 

discrepancy between theory and 

experiment, at least as far as the large differences between cases Iandll 
are concerned, is partly explained by the fact that the beams of primary 
and of secondary radiation are never strictly parallel. Hence, E is never 
exactly parallel to e or to the plane of the r's. It is easily pioved that 
case II is more influenced by this circumstance than case I (468). 
Keussler's measurements were made by a photoelectric method and 
were probably more accurate than the older photographic determina- 
tions, inasmuch as he he tried to eliminate all causes which might tend 
to decrease the degree of polarization. He assumed the discrepancies 
between his results and the theoretical values to be real (80 % in case I 
instead of 100%), and was the first to propose the hypothesis that 
they were caused by the hyperfine structure of the line. A degree of 
polarization of nearly 100 % (98.8 %) could be obtained only when the 
magnetic field strength was raised to 700 gauss (773,774,1067,1896- 
1898). 

Similarly, degrees of polarization much below 100 % were found 
in weak magnetic fields for the resonance lines of cadmium, zinc, and 
calcium. And again, the polarization of the cadmium line 3261A 
increased in a strong magnetic field to 95 % or nearly the theoretical 
value. Soleillet has shown that the polarization of this cadmium line 
is the same in stationary vapor or in an atomic ray, if the conditions 



66 MONATOMIC GASES AND VAPORS 

Table 7 



Degree of Polarization p of the Resonance Lines 
Cd, Zn, and Ca 


OF 




Cd 


Zn 


Ca 


* in % 


3261 2288 
87 76 


3076 2139 
67 74 


4227 
76.5 







of excitation are otherwise the same (1538). The measurements for 
the calcium line were made under rather unfavorable technical 
conditions (badly defined vapor pressure, presence of 3 mm of helium). 
It is, therefore, very doubtful whether the author was justified in 
extrapolating the experimental results to infinitely low vapor pressures, 
so as to arrive at a limiting value of polarization equal to 95 % (354, 
968,1326,1339,1567). 

Case II is cylindrically symmetrical with respect to the X-axis; 
therefore, the polarization of the fluorescence is in this case independent 
of the polarization of the exciting radiation. 

If the orientation of H is varied continuously from position I to 
position II, it passes through a position III, in which the vector E 
excites the oscillators e and r with equal strength ; hence, they emit 
radiation of equal intensity and the fluorescence light is completely 
depolarized. For orientations of H between I and III, and between II 
and III, respectively the azimuth of polarization is rotated continuous- 
ly from the direction of the X-axis or of the Z-axis, respectively, into 
the direction III, while the degree of polarization drops simultaneously 
from its maximum value down to p = 0. Figure 23 shows the excellent 
agreement between the calculated and the observed values of p. The 
points on the curve are the measured values at the angle <p between H 
and Z ; the curve itself is derived from the equation : 

p = (7.5 cos 2 cp — 3.75 sin 2 ?>)/(9.5 sin 2 <p — 5.75 cos 2 q>) (16) 

The numerical coefficients are chosen so that for g> = 0°, 55°, and 90°, 
p = 79 %, %, and 65 %, corresponding to the values which had been 
observed for these angles {1176). 

Similarly, the degree of polarization of the resonance radiation 
can be worked out for any other relative orientation of H and E, in 
good agreement with the experiments. 

Case IV, in which H is parallel to the direction of observation 
(parallel to the Y-axis in Figure 22), is of particular interest for small 



THE MERCURY LINE 2537a 



67 



values of H. Only the two circularly polarized waves which have 
opposite directions of revolution and are emitted by the two rotors r-^ 
and r 2 are observed under these conditions. In a weak magnetic field, 
these two components cannot be resolved by ordinary spectroscopic 
methods; none the less, their frequencies are slightly different. There- 
fore, the relation between their phases is not constant and the fluo- 
rescence is more or less depolarized. If, however, the radiation emitted 




Fig. 23. Polarization of Hg-resonance radiation 

as a function of <p, the angle between H and E 

(Olsen). 



in the direction of the Y-axis by a resonance lamp (with E parallel td 
Z and H parallel to Y , according to case IV) is passed through an 
absorption cell containing mercury vapor, the resonance radiation is 
not absorbed if this cell is subjected to a magnetic field H', of equal 
strength but antiparallel to H ; the radiation is strongly absorbed if H 
and H' are parallel. This experiment proves that the apparently un- 
polarized fluorescence of case IV really consists of two circularly 
polarized, very close components. If the same experiment is repeated 
with H and H' parallel to X (as in case II), a reversal of the direction 
of H' has no effect on the absorption of the fluorescence radiation; 
this last observation shows that no angular momentum is transferred 
from the circular oscillators to the field of radiation, if the quanta are 



68 



MONATOMIC GASES AND VAPORS 



emitted in a direction perpendicular to the lines of force of the 
magnetic field* (transversal Zeeman effect) (439). 

Kastler has repeated these experiments with the same results 
for the D-lines of sodium vapor. It should be mentioned that the 
principle of the method had been independently suggested by Ruark 
and Urey (725,1388). 

26. Anomalous Zeeman Effects. The simple model used in the last 
section does not avail for the representation of more complicated 
Zeeman effects and of the resulting polarization of fluorescence 



r 3 r 




c/ i 






1 


2 


3 




1 


II 


1 




<o> 




\J 








' 


' 



yp. 



3 2 s, 



. a' 




— , + 

1 


4' 

1 


3' 
II 


1 

12' 

!• 

■ 1 


1' 

JL 
^' 1 




A. 


' 















m 






3*'. - 






+ T 


b 












~2 


a 

1 2 
i 1 


3 

II 


14 

'll 


5 6 

i 1 
xJKJ 


3 

1;'. 


3 2 S. 


._ A 





Fig. 24. 

Magnetic sublevels 

for the Hg-line 2537A. 



Fig. 25. 
Magnetic sublevels 
for the Na-line D^ 



Fig. 26. 
Magnetic sublevels 
for the Na-line D,. 



radiation. Experimental observations are easily interpreted, however, 
by introducing the well-known Lande- schemes of magnetic energy 
sublevels into which the various levels of a Grotrian diagram split 
under the action of a magnetic field. Zeeman schemes of this type are 
reproduced in Figures 24 to 27 for the mercury resonance line, for the 
two D-lines, and for the green thallium line. Transitions in which the 
magnetic quantum number m remains constant correspond in these 
schemes to emission or absorption of radiation plane polarized parallel 
to H (77-components) ; transitions in which m is altered by ± 1 corre- 
spond to circular polarization (a-components) . If, by an absorption 
process, the atom is raised to a Zeeman level from which only -n- or 
only CT-transitions originate, the secondary radiation is totally polarized 
(as in Figure 24) . If transitions of both kinds can originate from the 

* It is not yet possible to decide whether some qualitative experiments 
communicated by Yen are connected with Fritsch's experiments, which have 
been related above. Yen found that the intensity of the resonance radiation 
emitted by an atomic ray of mercury varied according to whether a magnetic 
field was oriented parallel or antiparallel to the exciting beam (igig). 



ANOMALOUS ZEEMAN EFFECTS 



69 



excited level (as in Figures 25 to 27), the secondary radiation is partial- 
ly or completely depolarized, even if the exciting light is completely 
plane polarized. The degree of polarization can be computed from the 
relative probabilities of the individual transitions which occur from 
the various excited levels. Thus, the fluorescence of the D r line should, 
according to Figure 25, always be completely unpolarized, as has been 
confirmed experimentally. On the other hand, the D 2 -line is partially 
polarized in cases I and II [467,1282). If the theoretical values for the 
relative intensities of the Zeeman components are used for the evalu- 



2 d 



«4 3 



6p> ;*.. 



tt+ 



rrr 



1 ' 



I2T68 



1 1 



I li 

I 1 
1 I I 

182218 668866 

ii'! 



n ' 1 



*4l 



TTTT 



-^4 



:ii_ 



T 



JiZ- 



!-M 



rs, 



6P, 



Fig. 27. Magnetic sublevels for the Tl-line 5350A [Guelke {547)] . The 
numbers indicate the relative intensities of the components. 



ation of p, without taking into account the influence of hyperfine 
structure, the degree of polarization of D 2 is 60 % in case I and 42 % 
in case II. 

If, as in most experiments, the two D-lines are not separated, and 
if it assumed that the ratio of the intensities of ~D 1 and D 2 is 1 : 2 in 
the spectrum of the exciting radiation as well as in the absorption 
spectrum of the resonance lamp, the intensity of D x would be only 1 / i 
of the intensity of D 2 in the resonance radiation. The resulting 
polarization of the total resonance radiation would be 50 % in case I 
{351,352). 

In strong magnetic fields (H larger than 150 gauss), Datta ob- 
tained p = 58 %, using D 2 alone for excitation, and Larrick obtained 
p = 46.25 % under excitation with both .D-lines in a magnetic field 
of 350 gauss. The agreement with the theoretical values is good, 
inasmuch as in Larrick's experiments the intensity of D x was probably 
greater than has been assumed, thus decreasing the observed value of 
p. In weak magnetic fields (H = 10 gauss), however, Ellett and his 
collaborators never succeeded infindinga degreeof polarization greater 
Pringsheim 3 



70 MONATOMIC GASES AND VAPORS 

than 16.3% under excitation with both D-lines, corresponding to 
p = 21 % under excitation with D 2 alone. 

The degree of polarization of the resonance radiation is greatly 
dependent on the vapor pressure. According to Datta, the polarization 
of the D 2 -line resonance tends with decreasing sodium vapor pressure 
toward 60 % even in vanishing magnetic fields. The lowest pressure 
at which he was actually able to make a measurement was 3- 10 -7 mm 
at 115° C and the correspondent p value in magnetic fields below 1 
gauss was 33 %. Ellett's and Larrick's latest measurements, however, 
were made at an even lower vapor pressure (10 -8 mm at 80° C), with 
the results mentioned above (2 59, 3 53, 866). 

At the time of their publication Datta's results were in closer 
agreement with the theoretical expectations. However, because of the 
influence of the hyperfine structure, these were correct only for strong 
magnetic fields. In a field of 12,000 gauss Ellett even obtained a 
degree of polarization of 100 % for the resonance emission of the D 2 - 
line. With the lines of force parallel to the exciting beam (case II), 
only the two inner cr-components (2 and 5) were excited, while the two 
outer o-components (1 and 6) were displaced so much that they were 
not covered by the narrow line in the primary radiation. Thus, no 
atoms were brought into the magnetic levels corresponding to« = 
+ 1 l i and m = — 1 / i and the ^-components were completely missing 
in the secondary emission. (Compare Figure 26). 

For the second unresolved doublet of the main series of sodium 
excited with nonpolarized radiation, Ellett and Heydenburg found 
the polarization to be 30 % in a magnetic field of 80 gauss oriented as 
in the last experiment. This is again in satisfactory agreement with 
theory. In a vanishing magnetic field the polarization dropped to 10 % 

27. Negative and Circular Polarization. If the exciting absorption 
and the fluorescence emission correspond to different electronic 
transitions, the polarization of the fluorescence can become negative : 
the fluorescence can be partially polarized in a direction perpendicular 
to the polarization of the primary light. Of the four lowest electronic 
levels of thallium shown in Figure 9, 2 S 1/2 splits into two magnetic 
sublevels according to the rules of Section 12. Hence, the emission lines 
originating from 2 S 1/2 must always be completely depolarized, like the 
D^line of sodium. 2 P 1/2 splits also into two sublevels, while 2 P 3/2 and 
2 D 3/2 are resolved into four magnetic levels. The line 6 2 Z) 3/2 -> 6 2 P 1/2 
behaves, therefore, as far as the Zeeman effect and the polarization are 
concerned, like the sodium D 2 -line. If thallium vapor is excited by the 
absorption of the line 2768A under the conditions of case I, transitions 



NEGATIVE AND CIRCULAR POLARIZATION 



71 



occur only to the magnetic levels c and b of the state 2 D 3/2 (Figure 27). 
The intensity of the a-components of the line 3530A, which originates 
from these magnetic levels, is much larger than that of the 7r-com- 
ponents,and thus the fluorescence line3530A is, under these conditions, 
partially polarized parallel to X, while the exciting light is polarized 
parallel to Z {547) . 

Table 8 

Degree of Polarization of Thallium Lines 

in a Magnetic Field (Case I) 

P ^ % 



Wavelength 
in A 


p, observed 


p, computed 
without h.f.s. 


p, computed 
with h.f.s.* 


2768 
3530 
3776 
5350 


+ 35 

— 60 






+ 60 

— 75 






+ 33.3 + 35.1 
— 41.8 — 48.8 





* h.f.s. = hyperfine structure. 

The lines of the visible mercury triplet show a behavior similar to 
that of the thallium lines, though the case is still further complicated 
by stepwise excitation. If the resonance lamp contains nitrogen, the 
ground level for the second absorption process is almost exclusively 
the metastable state 6 3 P , which does not split up in a magnetic field. 
Under excitation by the isolated line 4047A, only the magnetic level 
m = of the state 1 S S 1 is reached is case I. In the subsequent fluo- 
rescence emission the line 4047A should theoretically (and disre- 
garding the h.f.s.) show a positive polarization of 100%. The polari- 
zation of the line 4358A should, under similar conditions, also be 
100%, but negative, since only the two cr-components / and g of 
Figure 28 contribute to the emission (the transition Am = being 
forbidden for 47 = 0); finally, the polarization of the line 5461 A 
should, under these conditions, be + 14.3 %. Table 9 shows a compari- 
son between the experimental results obtained by Richter and the 
theoretical values. In case II, which has not been investigated 
quantitatively, the line 4047A should again have a positive polari- 
zation of 100 %, while the line 4358A should show a partial negative 
polarization because of the relatively greater intensity of the n- 
components {578,729,1037,1357,1530, 1531) . 

If no nitrogen is present, the state 6 3 P lt which is directly reached 
by the absorption of the resonance line, becomes the starting level for 



72 



MONATOMIC GASES AND VAPORS 



Table 9 

Degree of Polarization of the Mercury Triplet Lines 7 3 S 1 -> 6 3 P 0)1 , 

in a Magnetic Field (Case I), Excited Stepwise, 

in the Presence of Nitrogen 

P in % 



Wavelength 
in A 


p, observed 


p, calculated 
without h.f.s. 


p, calculated 
with h.f.s. 




4047 
4358 
5461 

2957 
3131 
3663 


4 77 

— 48 
4- 13 

4- 75 

— 22 
4- 45 


4- 100 

— 100 
4- 14 

4- 100 

— 100 
4- 14.3 


+ 84.7 

— 44.6 
+ 3.4 

4- 84.7 

— 44.6 
4- 3.4 



the second absorption process. 6 3 P 1 splits into three magnetic levels 
(Fig. 28), of which (because of Am = ± 1) only the levels m = 4- 1 
and m = — 1 are populated in case II. From there, level m = of 
the state 7 3 S X alone can be reached by absorption of the line 4358 



4047 



4358 



5461 



7^, 0- 



d e f g h 



■6 7>, 



1 








1 
1 

1 












♦ 



* I m n o p q r s 



2 J 

e 3 p,o- 



I I I I 2 

1 1 1 1 II 



6 6 1 3 8 3 16 6 

1 II 1 1 II I i II 1 



Fig. 28. Magnetic sublevels for stepwise-excited Hg-fluo- 

rescence [Richter {1357)]. The numbers below the diagram 

indicate the relative intensities of the components. 

under the condition that, again, Am = ± 1. Only the a-components / 
and g of the line 4358 and the -n -component of the line 4047 originate 
from this level, so that now the line 4358 is positively, and the line 
4047 is negatively, polarized. This was actually observed by Kastler; 
if nitrogen was admitted into the observation chamber, the sign of 
the polarization of the two lines was reversed (7^8). 

The phenomena would be still further complicated if pure 
mercury vapor were excited stepwise by the two lines 2537 and 4358A, 



NEGATIVE AND CIRCULAR POLARIZATION 73 

polarized with their electric vectors perpendicular to each other. This 
problem has been suggested by Kastler, but, so far, no measurements 
have been made {726). 

Richter measured the degree of polarization of the line 4358A 
under stepwise excitation in the presence of nitrogen for various 
orientations of the vectors E and H. He investigated, also, the polari- 
zation of the ultraviolet triplet 7 s D 1 -+ 6 3 P 0jli2 (2967, 3131, and 
3663 A) (compare Table 9). The result of all these investigations was 
that the observed polarization agreed qualitatively with values 
predicted by theory, especially as far as the sign was concerned, while 
there were numerous and considerable quantitative discrepancies 

(1357) • 

The excitation of resonance radiation by circularly polarized light 
produces results of particular simplicity if the direction of observation, 
the direction of the magnetic field, and the direction of the primary 
radiation coincide. Under these conditions, only the transitions corre- 
sponding either to Am = + 1 or to Am = — 1 are excited, depending 
on the sense of rotation of the electric vector of the primary light." 
From the magnetic levels populated by these transitions the same 
CT-components which were absorbed are re-emitted. A 7r-component, 
which may also be emitted, contributes no radiation in the direction of 
observation.* Hanle obtained complete circular polarization of the 
mercury resonance line excited under these conditions and a circular 
polarization of 87 % for the two D-lines of sodium vapor in a longi- 
tudinal magnetic field of 600 gauss. The, unimportant deviation from 
the theoretical value in the second case was due to the incomplete 
parallelism of the primary and the secondary radiation {573)- 

The analogue to "negative" polarization is provided also in this 
instance by the green thallium line, when it is excited by absorption 
of the ultraviolet line 3776A. If the exciting light is polarized circu- 
larly clockwise, the partial polarization of the fluorescence is counter- 
clockwise and vice versa [574). Stepwise excitation of the triplet lines 
of mercury by circularly polarized light produces, again, similar effects. 
Kastler has investigated the phenomena arising when circular polari- 
zation is applied in both stages of the excitation process in the absence 
of nitrogen. In his experiments, circularly polarized radiation of 
wavelength 2537 and 4358A entered a resonance lamp through op- 
posite windows; a magnetic field of 10 gauss was applied with its lines 
of force parallel to the exciting beams. If the circular polarization of 

* This is correct only if / = or / = \ for the ground state ; the condition 
is, however, fulfilled in all cases which are treated in this section. 



74 MON ATOMIC GASES AND VAPORS 

the primary radiation of wavelength 2537 is counterclockwise, corre- 
sponding to Am = + 1, the excited level of 6 3 P i has the magnetic 
quantum number m = + 1, since the magnetic quantum number of 
the ground state is 0. No magnetic level with the quantum number 
m = 2 exists in the state 7 3 S 1 to which the atom is raised from 6 3 P 1 
by the subsequent absorption of the line 4358A. Hence, no stepwise 
excitation is possible under these circumstances if the circualr polari- 
zation of the primary radiation of wavelength 4358A is also counter- 
clockwise. If, however, the polarization of this radiation is clockwise, 
stepwise excitation does occur, since, because Am = — 1, the atom 
is raised into the actually existing magnetic level of the state 7 3 5 x with 
the quantum number m = 0.* These oversimplified theoretical pre- 
dictions are not quite correct, due to the influence of hyperfine 
structure. However, Kastler found experimentally that the emission 
of the line 4358A was very much stronger if the circular polarization 
of the two exciting lines had opposite signs (y2y-j2g). 

28. Vanishing Magnetic Fields. It has already been mentioned that 
quantum. theory was at first unable to make any predictions regarding 
the polarization of resonance radiation in the absence of an external 
force which determines the spatial orientation of the atoms. Since the 
conditions prevailing for H = can be arrived at by the adiabatic 
disappearance of a field of fortuitous orientation, it seemed natural to 
expect that with no magnetic field the degree of polarization should be 
lower than with a magnetic field oriented as in case I or II. If the local 
magnetic fields caused by the surrounding atoms are oriented at 
random, one should, according to Heisenberg, obtain for the mercury 
resonance line p = 27-% (instead of 100 %), for D 2 , p = 14 % (instead 
of 60%), and for Dj, p = (Sgs). This calculation did not take the 
hyperfine structure into account. However, Wood and Ellett had 
found, in their earliest experiments, the same degree of polarization of 
the mercury resonance line for case I in strong magnetic fields and 
with H = 0. Keussler confirmed this result and measured the angular 
intensity distribution of the resonance radiation in the plane perpen- 
dicular to the direction of the exciting radiation (plane Y-Z) under 
the same conditions. If the fluorescence emitted in the direction Y 
were totally plane polarized, its intensity should drop to zero in the 
direction Z. Actually, it drops to about 1 / w of the maximum intensity. 
The total intensity distribution can be represented by the superposition 
of an unpolarized radiation /„, which does not depend on the direction 

* The light emitted from this level has partially clockwise and partially 
counterclockwise circular polarization, resulting in complete depolarization. 



H.F.S. AND POLARIZATION OF RESONANCE RADIATION 75 

of the observation, and a plane-polarized radiation I p , according to 
the equation: 

I = /„ + I p sin 2 <p (17) 

<P is the angle between the direction of observation and E. Neglecting 
the term /„, which could not be explained at that time, Equation (17) 
represents exactly the angular intensity distribution of the radiation 
which an isotropic oscillator would emit under the action of an incident 
plane-polarized wave. This distribution would not be changed by the 
presence of a magnetic field with lines of force parallel to the oscil- 
lations (H parallel to E). Therefore, Bohr introduced the new hypo- 
thesis into quantum theory that, in the absence of space quantization 
by an external field, the radiation of an atom should have the same 
polarization as the radiation emitted by a corresponding classical 
oscillator under the action of a magnetic field which would not 
influence the vibration of the oscillator (128). 

In this form the rule cannot be applied to atoms with anomalous 
Zeeman effects, since no classical oscillator with corresponding pro- 
perties exists. Heisenberg generalized the rule in the following way : in 
the absence of an external field, the polarization of the radiation of an 
atom is the same as in the presence of a magnetic field which leaves the 
total symmetry unaltered. If the primary radiation is plane polarized, 
H should be parallel to E; if the primary light is unpolarized or circu- 
larly polarized, H should be parallel to the direction of the exciting 
light ray {595). This law of "spectroscopic stability" holds, of course, 
only if the auxiliary magnetic field is not strong enough to produce a 
Paschen-Back effect of the hyperfine structure. Only then the complete 
disappearance of the magnetic field leaves the conditions unaltered. 

29. Influence of Hyperfine Structure on Polarization of the 
Resonance Radiation. Ellett and McNair proved that the anomalous 
Zeeman effects of individual hyperfine-structure components of the 
mercury resonance line cause the difference between the polarization 
which is observed in a field-free space and the expectation of the pri- 
mitive theory {355,358,969,1040). On spectrograms obtained with a 
Lummer-Gehrke plate, the degree of polarization of components 
— 10.4,0, and + 11.5 appeared to be practically 100% for vanishing 
values of H under the conditions of case I. Simultaneously, the degree 
of polarization of components —24.5 and +21.5 was certainly below 
60%. Figure 19 shows that component —24.5 is exclusively, and 
component +21.5 mainly, due to the odd isotopes Hg 199 and Hg 201 . 
The nuclear momenta of these components are i — 1 / 2 and 3 / 2 , re- 



76 MONATOMIC GASES AND VAPORS 

spectively, and their magnetic quantum numbers are, therefore, not 
to be derived from J but from f = J + i. The /-values in Figure 20 
show that component A of Hg 199 has a Zeeman effect of the same type 
as D l7 and component B one of the same type as D 2 (Figures 25 and 26, 
in both cases neglecting the h.f.s. of the D-lines). Hence, p = for 
component A and p = 60 % for component B. Making use of similar 
considerations, the degree of polarization of components a, b, and c 
of the isotope Hg 201 can be determined, b coincides with the single line 
of the isotope Hg 198 , which is thereby slightly depolarized. The total 
polarization of the unresolved mercury resonance line can be computed 
from these data if the relative concentration of the isotopes and the 
intensity distribution of the h.f.s. -components in the exciting radiation 
are taken into account. Two limiting cases are relatively easy to deal 
with. Either the resonance line in the primary radiation is so broad 
that its intensity can be regarded as being constant over the whole 
width of the hyperfine structure of the absorption line, or the primary 
light source is itself a resonance lamp, and the intensity distribution of 
the exciting line is the one represented in Figure 19. In the first case 
the degree of polarization of the unresolved radiation is, according to 
the calculation of Larrick and Heydenburg, 84.7 %, while in the second 
case it is 88.7%. This explains the decrease of the degree of polari- 
zation of the mercuiy resonance line which Olson observed with 
increasing current density in the exciting mercury arc. 

Table 10 lists the calculated degree of polarization of the individu- 
al components for the first case. 

Table 10 

Degree of Polarization Calculated for the H.F.S. -Components of 

the Mercury Resonance Line 



Component 
P in % 



+ 21.5 + 11.5 
55.9 100 



— 10.4 

100 84.8 



25.4 
51.4 



If the lines in the spectrum of the primary light source are more 
or less self-reversed, the intensities of the single components belonging 
to the most abundant isotopes, Hg 200 and Hg 202 , are much more reduced 
than those of the components belonging to the odd isotopes. Under 
such conditions, the resulting polarization of the unresolved resonance 
radiation may be much smaller than the values calculated by Larrick 
and Heydenburg (358, 867a, 96g, 1176,^36). 

The agreement between the observed degree of polarization and 
the values calculated from the hyperfine structure is much less 



H.F.S. AND POLARIZATION OF RESONANCE RADIATION 77 

satisfactory for the stepwise-excited Hg-triplets 7 3 S X -> 6 3 P , 2 and 
7 3 Z)j ->6 3 -P 012 (compare Table 9). The discrepancies, which are 
particularly large for the transitions leading to 6 3 P 2 (the lines 5461 and 
3663A), certainly exceed the errors which can occur even in the 
determination of rather small degrees of polarization. Nor is it probable 
that they are caused by anomalous intensity distribution in the 
exciting line, for instance, by strong self-reversals and it seems likely 
that still unknown factors have to be taken into account. 

The cadmium lines 2288 and 3261 A differ from the mercury reso- 
nance line in that most of their h.f.s. -components are exceedingly 
close. The components of the line 2288 A have not yet been resolved 
spectroscopically ; the line 3261 A has three components (AX. = — 18.0, 
0, + 17- 10~ 3 A), which are evidently due to the splitting of the upper 
level 6 3 P 1 , since the ground state 6 1 S is common to both lines. 
However, the fact that the degree of polarization of the line 2288A 
never exceeds 76.3 % for H = proves that also for this line an 
influence of hyperfine structure has to be considered (357). According 
to Schueler, the nuclear spin of the odd isotopes of Cd is i = x / 2 . 
Taking this value for granted, it is possible to work out the relative 
concentration 7 of the even and the odd isotopes from the measured 
degree of polarization of the line 2288A. From the value 7 = 2.6 which 
is obtained by this method, the degree of polarization of the other 
resonance line can be computed; the value thus calculated (86.4%) is 
in excellent agreement with the observed values (86 to 87%)* (1525, 

1534)- 

Because of the small separation of the components ot the cadmium 

h.f.s.-levels, the Paschen-Back effect occurs in relatively weak 

magnetic fields. Table 1 1 shows p as a function of H. For H = 563 

gauss, the influence of the hyperfine structure is practically eliminated 

and the theoretical value of p = 100% is almost reached (609,1039, 

1536). 

From the curve representing p as a function of H, separation of the 
h.f.s.-levels of the term 5 3 P 1 , which has not yet been determined 
directly, can be derived; the calculated value is 12.6- 10~ 3 A. 

The influence of the hyperfine structure causes a relatively strong 
depolarization of the resonance radiation of Tl and Na, which consist 
exclusively of odd isotopes. From the nuclear spin i = Va which is 

* From the relative intensities of h.f.s. -components of other Cd-lines, 
Schueler derived y — 3.34. The corresponding values of p = 80.5% for the line 
2288A and p = 89% for the line 3261 A can hardly be brought into agreement 
with the observations. 
"Pringsheim 3* 



78 



MONATOMIC GASES AND VAPRS 



Table 11 
Increasing Polarization of Resonance Radiation in Strong- 
Magnetic Fields Caused by the Paschen-Back Effect of Hyperfine 

Structure 



Cd 2288A 


NaD 


+ D, 


H in gauss 


P in % 


H in gauss 


P in % 





76.7 





16.48 


75 


77.3 


10 


16.3 


149 


79.9 


20 


21.37 


200 


82.5 


50 


34.54 


255 


86.2 


70 


38.86 


315 


89.1 


90 


43.0 


375 


92.1 


170 


45.7 


563 


95.0 


315 


46.25 


(~) 


(100) 


(*>) 


(50) 



ascribed to both Tl-isotopes, Tl 203 and Tl 205 , the degrees of polari- 
zation which are listed in Table 8 were derived by Ellett. For the 
figures under a, the exciting line is assumed to be resolved into its 
h.f.s.-components, while for those under b, the intensity is supposed to 
be constant over the whole width of the absorption lines. If a value of 
i larger than 1 / 2 , for instance i = 3 / 2 , were to be ascribed to one of the 
isotopes, the depolarization of the Tl-lines in Table 8 would become 
even larger. The agreement between the calculation and the experi- 
mental results is very poor; the latter would actually fit best with the 
nuclear spin number i = (as in the case of no h.f.s.), which is cer- 
tainly not correct (355). 

Sodium is known as a "pure" element with atomic weight 23. 
It should, therefore, be possible to derive the nuclear spin momentum 
i directly from the observed degree of polarization of the resonance 
radiation, without the introduction of any additional hypothesis. The 
value found by Datta for the maximum polarization in the absence of 
a magnetic field is in complete contradiction with all other measure- 
ments (259). Leaving it out of consideration, the best value for the 
unseparated D-lines seems to be p = 16.3 % or, for D 2 alone, 21 %. 
This leads directly to i = 1 . From other experiments (Stern-Gerlach 
effect and analysis of the Na 2 -bands), the momentum i = 3 / 2 is ob- 
tained. This, in turn, would correspond to p =• 15.4% for the un- 
resolved D-lines, which differs from the experimental value by more 
than the possible error. However, the h.f.s. -separation of the 3 2 P 3/2 - 
state of sodium is small, even in comparison to the natural width of 
the line which corresponds to the lifetime of the excited state 3 2 P 3/2 



DETERMINATION OF T FROM DEGREE OF POLARIZATION 79 

(t = 1.6- 10 -8 sec). Therefore, the h.f.s.-levels overlap and a resulting 
degeneration of the quantization must be taken into account. Doing 
this, Larrick obtained p = 16.25 for i = 3 / 2 , in complete agreement 
with the observations (356 ,611,612, 866, 867). Asin the case of cadmium, 
above, the distance between the h.f.s.-levels of Na 3 2 P 3/2 can be 
calculated from the change of the degree of polarization with in- 
creasing magnetic field strength ; the value thus obtained is A v = 
1.45- 10 -4 cm -1 (compare Table 11). 

The observed degree of polarization of 9.2% for the second 
doublet of the main series of sodium also does not agree with the 
nuclear momentum i — 3 / 2 , if no correction corresponding to the 
natural width of the lines is introduced. Assuming a line width corre- 
sponding to the plausible lifetime t = 3.05- 10~ 8 sec for 4 2 P, the theo- 
retical value of p becomes exactly 9.2 %. 

The degrees of polarization of the resonance radiation of rubidium 
(second doublet at 4202/ 15A) and cesium (first and second doublets at 
8521 and 4555A) correspond to nuclear momenta which agree approxi- 
mately with the values derived from other experiments {32,610) . 

Summarizing, it can be said that the disagreements between the 
observed degrees of polarization and the original calculations are in 
the main caused by the influence- of hyperfine structure. However, a 
number of discrepancies are still unexplained and the deviations can 
be completely accounted for only in those rare cases in which the 
nuclear momentum is known from other sources and in which the 
conditions are otherwise fairly simple as, for instance, for sodium. 

E. Determination of t from the Degree of Polarization 
in Weak Magnetic Fields 

30. Principle of the Method. In case IV, with the exciting radiation 
plane polarized parallel to Z and the magnetic field in the direction of 
observation, parallel to Y, the secondary radiation was assumed to 
consist of two incoherent circularly polarized components. This cannot 
remain true for very small field strengths, because, otherwise, the 
weakest magnetic field in the direction of observation would be 
sufficient for complete depolarization of the fluorescence. With 
vanishing field strength the degree of polarization must always tend 
towards the same limiting value, irrespective of the direction of the 
field. Actually, the depolarization of the resonance radiation is small 
in case IV, as long as the magnetic field is weak, and this depolarization 
Pringsheim 3** 



80 



MONATOMIC GASES AND VAPORS 



is accompanied by a rotation of the plane of polarization. Both effects 
increase with increasing field strength, and the last remainder of 
linear polarization disappears only when H exceeds a critical value, 
which differs greatly for various lines. 

Hanle explained this phenomenon on a semiclassical theoretical 
basis. Though his model cannot be claimed to be rigidly correct, it has 
the great advantage of being easily visualized. Hanle assumed that a 
linear "virtual oscillator" is excited instantaneously with maximum 
amplitude by the absorption of one quantum hi. From there on, the 
amplitude of the oscillator decreases continuously according to 
classical radiation-damping. If an oscillator of this nature is placed in 





Fig. 29. Precession of linear electric 
oscillator in a strong magnetic 
field perpendicular to E (Hanle). 



Fig. 30. Precession of a damped 

linear electric oscillator in a weak 

magnetic field perpendicular to E 

(Hanle). 



a magnetic field H, the lines of force being perpendicular to the vi- 
brations of the oscillator, it precesses like a spinning top around the 
lines of force. The resulting movement is a rosette of the type shown 
in Figure 29. The rotational frequency of this "Larmor precession" is : 



O 



H-e/2c-m 



(18) 



If the frequency of the precession is so small that the amplitude of 
the oscillation decreases appreciably during a complete revo- 
lution, the rosette does not retain its circular symmetry (Figure 30). 
A preferential orientation of the electric vector prevails which is, 
however, rotated by an angle d with respect to the initial direction of 
polarization Z. The larger the lifetime t, the smaller is the field strength 



DETERMINATION OF T FROM DEGREE OF POLARIZATION 



81 



which causes a complete rotation of the oscillator without appreciable 
loss of amplitude, and thus effects complete depolarization (571). 

It has since been shown that the strictly classical treatment of 
the behavior of an isotropic oscillator with normal Zeeman effect 
and the quantum-theoretical treatment of the general case lead to the 
same results (150-161,164,1742). 

In general, the left side of Equation (18) must be multiplied by 
the "splitting factor" g, which is, as already mentioned, 3 / 2 for the 
mercury resonance line 2537A and for the analogous lines of other 
metals (Cd, Zn, Ca) ; it is 2 / 3 for the line D 2 of sodium. 

If p is the degree of polarization in the absence of a magnetic 
field, a magnetic field H in the direction of observation reduces the 
degree of polarization to : 

P =Po/V 1 + (2ogT)« (19) 

Simultaneously, the angle d, by which the plane of polarization is 
rotated, becomes: 

d = 1 / a arctan 2ot (20) 

If the "apparent degree of polarization" p, is measured instead of p 
(compare Section 8), Equation (19) has to be replaced by : 



Pz=Pjll + {20gT)*l 



(19a) 



31. Experimental Results. The validity of these formulas has been 
checked quantitatively by Keussler and by Olson for the mercury 



100 




1.2 gauss 

Fig. 31. Depolarization (continuous line) and 
rotation of plane of polarization (broken line) 
of Hg-resonance radiation observed in the 
direction parallel to the magnetic field H 
(Keussler). 



82 



MONATOMIC GASES AND VAPORS 



resonance line. Here also, the influence of the h.f.s. must be taken into 
account. Assuming that the value of t was identical for all h.f .s.-levels 
of the state 6 3 P 1 Mitchell derived a theoretical curve which agrees 
within the limits of error with the curve of Figure 31, which was ob- 
tained under the assumption that there is only one kind of isotope 
with * = 0, and that, for reasons unknown, the polarization is only 
80 % instead of 100 % for H = (772,1176). 



20 



16' 



§'0. 





f " 


-'-"*""" 


-• 




1 


'"\q 








1 
1 

/• 
-/ 
/ 
/ 
' 1 


1 


1 


4 

' — ■ — 



8 
H in gauss 



16 



Fig. 32. Depolarization (continuous line) and rotation of 

plane of polarization (broken line) of sodium resonance 

radiation observed int the direction parallel to the 

magnetic field H. 

Mrozowski determined the angled as a function of H for the h.f.s.- 
components of the mercury line excited separately, and derived from 
these measurements lifetimes for the various levels of 6 3 Pj, which 
differed from each other by almost 50 %. It must, however, be taken 
into consideration that the splitting factor for the Zeeman effect of the 
isotope Hg 199 is not 3 / 2 but 1 ; introducing this correction, Mitchell has 
shown that Mrozowski's measurements prove directly that all h.f.s.- 
levels have the same lifetime (1040,1071). 

Olson used a second method for the determination of the value 
of t for the mercury resonance line. The exciting light was polarized 
parallel to the direction of observation Y, and H was parallel to Z. 
For reasons of symmetry p, under these conditions, must be zero for 
H = 0, and the observed fluorescence intensity must be due ex- 
clusively to the odd isotopes. With increasing field strength, the 
o-components of all isotopes are increasingly excited and a maximum 
degree of polarization parallel to X is obtained at high field strengths. 
The value t = 0.98- 10 -7 sec obtained by Olson is appreciably below 



DETERMINATION OF T FROM DEGREE OF POLARIZATION 



83 



Keussler's value: t = 1.1 • 10 -7 sec, but Mitchell showed that Olson's 
results can be represented satisfactorily by a value of t = 1.08- 10 -7 
sec {1176). 

If the lifetime of an excited state is shorter, stronger magnetic 
fields must be applied to obtain a certain degree of depolarization or a 
certain angle of rotation d. A comparison of the scales of abscissas 
used in Figures 31 and 32 shows at once that the life of the D-lines is 
considerably shorter than the life of the mercury resonance line, which 
is an intercombination line with a smaller transition probability. The 
lifetimes of the intercombination resonance lines of cadmium and 
zinc are longer still, and, therefore, much weaker magnetic fields in the 
direction of observation suffice for a complete depolarization of the 
fluorescence {1533,1535,1540,1791b) . On the other hand, the lifetimes 
of singlet resonance lines which originate from the states 1 P 1 are a great 
deal shorter. 

Table 12 
Lifetimes of Excited States of Hg, Cd, Zn and Ca 
(t in sec.) 



Combining 
terms .... 


S P-'S„ 


'P-'So 




Element 


Hg- 


Cd 


Zn 


Cd 


Zn 


Ca 


Resonance 
line (in A) . 


2537 


3261 


3076 


2288 


2139 


4227 


H* in gauss . 


0.4 


0.02 


5-10- 4 


150 


? 


17 


t derived 
from H* . . 


1.1 -lO" 7 


2.3-10-* 


io- B 


lO" 9 


? 


3.5- lO" 9 


t derived 
from other 
methods . . 


1.08-10-'t 
1.14- 10-'j= 


2. 5-10- 6 § 
2.14-10" 6 || 




2-10" 9 » 


< io-'tt 





t Garrett, alternating voltage method; Kopfermann and Tietze, absorption. 
=j= Ladenburg and Wolfsohn, anomalous dispersion. 

§ Kuhn, magnetic rotation; Koenig and Ellett, atomic beam method. 

|| Webb and Messenger, alternating voltage method. 
U Kuhn, magnetic rotation; Zemansky, absorption, 
ft Soleillet, atomic beam method. 



All observations concerning measurements of lifetimes by fluo- 
rescence methods are collected in Table 12. The "half-value field 
strength" H* is the field strength by which the degree of polarization 
is reduced to one half of its value in the absence of a magnetic field. 



84 MONATOMIC GASES AND VAPORS 

The relation between H* and t according to Equations ( 1 8) and ( 1 9) , is : 

t = \/ 3 mc/gH*e (21) 

Accurate measurements of lifetimes below 10 -7 sec are very difficult 
because of the minuteness of the magnetic fields by which depolari- 
zation is produced, and hardly more than the order ol magnitude of 
t can be warranted. 

As already mentioned, the fluorescence excited by the line 3261 A 
in an atomic beam of cadmium is "carried along" by the beam. Under 
these conditions the distance over wich an atom -travels before .it 
emits the fluorescence line is proportional to the time elapsed since 
the moment of excitation. If a magnetic field parallel to the direction 
of observation and perpendicular to the atomic ray is applied, the 
Larmor rosette of Figure 30 is drawn out along the atomic ray. If t 
is determined directly from the decrease of intensity along the ray, the 
splitting factor g can be calculated according to Equation (21) from 
the angle of rotation of the direction of polarization, which is measured 
on different points of the ray. Soleillet obtained g = 1.75 by this 
method. Considering the difficulty of the observations, the result is in 
satisfactory agreement with the theoretical value of g= 1.5 (1533-1535). 

Hanle and Richter have tried to derive the half-value period of 
the fluorescence of the mercury triplet 5461, 4358, 4047A from the 
depolarization of the lines in a longitudinal magnetic field. They ex- 
cited the fluorescence stepwise in the presence of nitrogen and ob- 
tained the surprising result that the green line seemed to provide a 
value of t four times as long as the two other lines, despite the fact that 
they all originate from the same excited level. R. H. Randall confirmed 
this result independently, using a different method. However, 
Randall's experiments have since been repeated by several investi- 
gators, most thoroughly by Mitchell, and his conclusions have been 
proved to be erroneous. Richteralso admitted, in a later publication, 
that his measurements were not sufficiently reliable for sustaining his 
earlier statement. Hence, the assumption seems justified that the 
lifetime of the mercury atoms in the state 7 3 S' 1 is the same for the 
emission of each of the three visible triplet lines ; it is probably of the 
order of 5- 10~ 9 sec (441, 578, 1042,1336,1352). 

Eq. 19 can be applied if in a magnetic 'field the excited state splits 
into three levels, while the ground state is unaffected, so that the 
resulting Zeeman triplet differs from the normal Lorentz triplet by 
not more than a g- value different from 1. If, however, the Zeeman 
effect is more complicated, involving several values of g for the excited 



ALTERNATING MAGNETIC FIELDS 



85 



and the unexcited states, or if lines with unequal Zeeman effects are 
not resolved (D t and D 2 of sodium, h.f .s.-components of mercury, etc.), 
Equations (19) and (19a) must be replaced by the following more 
general equation: 



Pz = 



i k 



(22) 



in which the indices i refer to the various components and the indices 
k to the Zeeman subcomponents of each component. 

Using Equation (22), the lifetime of excited sodium in the states 
3 2 P 1/2 and 3 2 P 3/2 can be determined by measuring the depolarization 
or the rotation of the plane of polarization of the unresolved D-line 
resonance radiation in longitudinal magnetic fields. The experimental 
curves are reproduced in Figure 32 ; the values of t which were derived 
from these curves, and also those obtained by several other methods, 
are listed in Table 13. The relatively large deviations of Duschinsky's 
measurements from the others have already been mentioned in 
Section 22. 

Table 13 
Lifetime of Excited Sodium Emitting the D-Lines, Obtained by 

Various Methods 



Method 


Fluorometer 


Depolarization 
in magnetic field 






Hupfeld 


Duschinsky 




T-10 8 


1.5 


0.82 


1.35 


1.6 


1.48 



* Compare footnote to Table 12. 

t Computed by Ladenburg from all available measurements. 

32. Alternating Magnetic Fields. The results produced by a 
magnetic field are not changed if, instead of a constant field, an alter- 
nating field is applied by means of an alternating electric current in a 
solenoid, as long as the period of the alternating field is long compared 
with the period of the Larmor precession, which is determined by the 
field strength. If the frequency of the alternating field exceeds the 
frequency of the Larmor precession, the latter no longer produces a 
complete rotation during a half-period of the magnetic field ; the sense 
of revolution is reversed after each half-period and with increasing 
frequency the motion degenerates into an oscillation of decreasing 
amplitude around the direction of the vector E. If the fluorescence is 
observed in the direction of the magnetic field, the degree of polari- 



86 MONATOMIC GASES AND VAPORS 

zation is eventually the same as without a magnetic field. The larger 
the effective strength of the applied field, the larger is the Larmor 
frequency o and the higher becomes the frequency at which the 
limiting state is reached. 

For the mercury resonance radiation, Fermi and Rasetti found 
practically no depolarizing action by a field of 1 . 1 3 gauss at a frequency 
of 5- 10 6 seer 1 . With 1.87 gauss, the action of the magnetic field on the 
polarization was already appreciable, while with 2.13 gauss, the degree 
of depolarization was the same in the alternating and in a constant 
magnetic field. From the relation between the field strength, the 
frequency of the alternating field, and the corresponding depolari- 
zation of the resonance radiation, the frecuency o of the Larmor 
precession can be calculated. Satisfactory agreement between theory 
and experiment is obtained only if the splitting factor g = 3 / 2 is 
introduced into the calculation. Assuming a normal Lorentz triplet 
with g = 1 for the mercury line 2537A, the alternating field of fre- 
quency 5- 10 6 should become ineffective in depolarizing the resonance 
radiation only at a field strength of 3.2 gauss, and not, as is actually 
true, at 2 / 3 -3.2 = 2.14 gauss (385). 

Fermi's and Rasetti's results were confirmed qualitatively by 
Breit and Ellett. These observations show why Wood could not in- 
fluence the polarization of the mercury resonance radiation by the 
alternating magnetic field of a strong beam of sunlight : the magnetic 
field of the sun radiation, which according to Wood's calculation was 
of the order of 3 gauss, was much too small, considering the high 
frequency of infrared and visible light (163). 



F. Stark Effect in Resonance Radiation 

33. Direct Demonstration of the Effect. The splitting of a reso- 
nance line in an electrostatic field by the so-called Stark effect is, in 
general, very difficult to observe, because resonance lines correspond 
to transitions between the lowest electronic states of an atom; with 
the exception only of the hydrogen atom, these states are very 
insensitive to the action of electric fields. Paschen and Gerlach were 
unable to find conclusive evidence of a shift exceeding the limit of 
error (5- 10~ 5 A) for the mercury resonance line in a field of 14,000 volts 
per cm {1194). 

Brazdziunas used the much more sensitive Schein-Malinowski 
method for the investigation of the Stark effect of the mercury 



STARK EFFECT IN RESONANCE RADIATION 87 

resonance radiation. A mercury resonance lamp was exposed alternate- 
ly to the action of a transversal magnetic and electric field and the 
lines of the absorption cell were displaced gradually, either by a second 
magnetic field or by the admission of small quantities of atmospheric 
air into the cell. Brazdziunas was thus able to show that the a-compo- 
nents of the Stark effect are shifted as much in a field of 100,000 volts 
per cm as one of the a -components of the Zeeman effect by a magnetic 
field of 1.2 gauss, the displacement being in either case 5.4- 10 _4 A 
toward greater wavelengths. The displacement of the vr-component is 
not larger in a field of 140,000 volts per cm than the displacement of 
the o-components in a field of 60,000 volts per cm. Assuming that the 
shift is proportional to the square of the field strength, the displace- 
ment of the a-components is five times larger than that of the n- 
component. It was not possible to determine whether the ^-component 
was displaced in the direction of greater or smaller wavelength {157)- 

Ladenburg investigated the Stark effect in the absorption 
spectrum of sodium vapor by means of an interferometer. Applying 
a field of more than 100,000 volts per cm, he obtained a shift of the 
D-lines of about 0.01A. At least qualitatively, he succeeded also in 
proving the occurrence of an effect of the same order in the resonance 
radiation of sodium vapor; the light emitted by a sodium resonance 
lamp was appreciably less absorbed in a second cell containing sodium 
vapor if the resonance lamp was under the action of the electric field. 
By inserting a Nicol prism into the path of the resonance radiation, it 
could further be shown that the cr-components (polarized in the plane 
perpendicular to the lines of force) as well as the w-component (polar- 
ized parallel to the lines of force) are both more or less influenced by 
the electric field. The exciting radiationand thedirection of observation 
were both perpendicular to the lines of force in these experiments 
{806,856). 

The higher electronic states of most atoms are much more 
sensitive to the action of external electric fields and, therefore, series 
lines corresponding to transitions between such states show Stark 
effects which are much easier to demonstrate. When a field of 5,000 
volts per cm was applied by Terenin to a mercury resonance lamp which 
was excited stepwise by the full radiation of a water-cooled mercury 
arc, all lines which originated from the levels 6 3 D 123 and 6 1 £> 2 
(compare Figure 17) were missing in the fluorescence spectrum, 
although they were present when the electric field was not applied. 
The resonance line and the lines originating from the state 7 3 S X were 
not affected by the field. The suppression of certain lines is obviously 



88 



MONATOMIC GASES AND VAPORS 



due to the fact that they are displaced in the absorption spectrum of 
the resonance lamp by more than their width in the primary radiation. 
This width was of the order of 10~ 2 A and thus the Stark effect must 
have produced a displacement of at least the same order. The effect is 
due almost exclusively to the action of the electric field on the upper 
states of excitation {6 3 Dj and 6 1 D 2 ) (1632). 

34. Polarization of Resonance Radiation in Electric Fields. Accord- 
ing to classical electrodynamics as well as to quantum theory, an 
electric field parallel or perpendicular to the vibrations of an oscillator 



3^. 



3S, : 



m 

-2 



3^ 
1 



11 



-J 



m 

~2 



Fig. 33. Level diagram 

for Stark effect of 

Hg-line 2537A. 



Fig. 34. Level diagram 

for Stark effect of 

Na-line D t . 



^S, - 

Fig. 35. Level diagram 
for Stark effect of 



does not influence the polarization of the radiation emitted by the 
oscillator. 

The quantum numbers m which determine the spatial quanti- 
zation have the same absolute values for each electronic state of an 
atom in an electric and in a magnetic field. However, in an electric 
field the energies of the levels + m and — m coincide and, therefore, 
the Zeeman level schemes of Figures 24-26 have to be replaced, for the 
Stark effect, by those of Figures 33-35. Thus, the transitions from the 
levels m = + I and m = — I of the state 6 S P X to the level m = of 
the state 6 1 S produce radiations which are circularly polarized with 
opposite signs but have the same frequency. If both components are 
excited simultaneously by absorption of plane-polarized light, their 
radiation, of identical frequency, is coherent and combines into a 
single wave which is plane polarized in the same direction as the 
exciting radiation. The phenomenon is exactly the same as if the two 
rotors Tj and r 2 introduced into the model for the Zeeman effect 
(Section 25) were replaced by a single linear oscillator e' perpendicular 
to the oscillator e and to the lines of force F and having a frequency 
slightly different form the frequency of e. 

Consequently, an electric field F either parallel or perpendicular 
to the electric vector E of the exciting radiation, should not alter the 



PERTURBATIONS OF RESONANCE RADIATION BY COLLISIONS 89 

polarization of resonance radiation; the polarization should remain the 
same in the presence or in the absence of the field. Eailier experiments 
by Hanle and by Richter on the resonance radiation of mercury and of 
sodium seemed to disagree with these theoretical predictions. However, 
Suppe later showed that these results were erroneous and that if all 
necessary precautions were taken, an electric field had no influence 
whatsoever on the state of polarization of the mercury resonance 
radiation, as long as F and E were oriented so that only e or only e' 
was excited (as in cases I, II or IV) (572,576,1597,1856). 

If the angle ■& between F and E differs from or 90°, the two 
virtual oscillators e and e' are excited simultaneously, their amplitudes 
being equal for # = 45°. Since the frequencies of the oscillators are 
not quite the same, a slowly increasing difference of phase must arise 
in their radiation and the wave resulting from their superposition 
becomes increasingly elliptically polarized. In a weak electric field, 
this process is so slow as compared with the duration of the emission 
that the polarization of the observed fluorescence is partially ellipti- 
cal. (The phenomenon is observed at its best in the direction parallel 
to the exciting radiation, where the oscillators e and e' contribute 
equal intensities to the total fluorescence). In stronger electric fields, 
the depolarization is complete, as in the somewhat similar case of a 
longitudinal magnetic field. 

In combined electric and magnetic "fields the polarization or 
depolarization caused by the magnetic field alone is not altered by the 
presence of an electric field up to 150,000 volts per cm, as long as the 
latter is oriented so that it would not influence the polarization in the 
absence of the magnetic field. If, on the other hand, the resonance 
radiation is depolarized by an electric field of adequate orientation and 
strength, the polarization is not restored by a magnetic field of any 
orientation. (This result obtained by Suppe is also in contradiction 
with Hanle 's earlier publication). 



G. Perturbations of Resonance Radiation by Collisions 

35. Effective Cross Sections. Resonance radiation is unperturbed 
only if the excited atoms are not subjected to collisions or, more 
generally speaking, to any interaction with other molecules during 
the time interval between the absorption and the emission process. 
If this condition is not fulfilled, the consequences are of two kinds. On 
the one hand, the state of the excited atom is altered so that, if an 



90 MONATOMIC GASES AND VAPORS 

emission occurs at all, the emitted light has a different frequency. On 
the other hand, the corresponding energy difference must be balanced 
somehow by the perturbing molecule, which in most cases will gain 
energy but sometimes also may lose energy to the excited atom. 
Collisions by which excited atoms or molecules transfer their electronic 
excitation energy to the colliding particles are called "collisions of the 
second kind." The fluorescence which would be observed in the ab- 
sence of collisions is quenched by collisions of the second kind (418, 

786). 

If the "competing process" characterized in Equation (6), 
Section 4, by the probability a x is due to collisions, and if every 
collision of an excited atom quenches its fluorescence, a t is equal to 
the number z k of collisions and since z h is proportional to the partial 
pressure p of the quenching gas, the equation takes to form in which 
it was published by Stem and Volmer ( 1571) : 

I = 7 /(l + z k r ) = IJ(1 + m (p being a constant) (23) 

or with several quenching gases of partial pressures p lt p 2 . . . : 

7=/ /(l+A/'i+Aft + ---) ( 24 ) 

If the intensity of the fluorescence is reduced from its maximum value 
I to a value I by the partial pressure p x of the first gas, the intensity 
T is not quenched by the partial pressure p 2 of the second gas as much 
as the intensity I would be quenched by the same quantity of the 
second gas in the absence of the first gas. For, by the quenching action 
of the first gas, the natural lifetime of the excited state t has already 
been reduced to the value r x according to Equation (5) Section 4. Only 
qualitative observations are available concerning the simultaneous 
quenching action of two gases on the resonance radiation of monatomic 
vapors. The mercury resonance radiation is reduced to 1 / 20 by 4 mm 
of hydrogen. If the intensity of the fluorescence is already quenched 
considerably by 100 mm of nitrogen, the addition of 4 mm of hydrogen 
reduces the intensity only to about 1 / 5 of the value observed in the 
absence of hydrogen. The quenching efficiency of atmospheric air 
can be calculated correctly using Equation (24) and taking into 
account the individual quenching efficiencies of nitrogen and oxygen. 
However, quantitative measurements on the fluorescence of iodine 
vapor show that, at least in this instance, the conditions are more 
complicated than was assumed in deriving Equation (24). (Compare 
Section 65) (93,203,1167). 

By variation of the value of p in equation (23), a state can be 



PERTURBATIONS OF RESONANCE RADIATION BY COLLISIONS 91 

attained, corresponding to a pressure p*, in which / = £/ or t = 
l/z k . Since \jz k is equal to the average time between two collisions, the 
lifetime t of the unperturbed excited atoms is equal to the time at 
the "half-intensity pressure" p*. If r has been determined by another 
method, the number of quenching collisions z can be worked out from 
Equation (23). If this number is found to be smaller than the value z k 
which is derived from kinetic theory, it is to be assumed that not every 
gaS-kinetic collision is actually quenching, and an "efficiency e" 
smaller than unity can be introduced. However, if z is found to be 
larger than z k , one is forced to assume that the "effective quenching 
cross section" for the perturbance under consideration is larger than 
the gas-kinetic cross section. 

An atom in a certain excited state can have different effective 
cross sections for different kinds of interactions with other molecules. 
Thus, it is clear that these interactions are not collisions in the sense 
of mechanics, according to which a collision is defined as an approach 
to a well-determined distance. The interaction reaches, theoretically, 
into infinity, while its strength decreases according to laws which may 
be widely different in different cases. These laws determine for every 
distance r a probability W(r) according to which the energy transfer in 
question will occur within the unit of time. 

If an effective cress section a (or an effective radius q) is defined 
by the equation : 



a = nQ € 



= / rW(r) dr (25) 



it can be shown that this value plays the same part for the "optical 
collisions" as the gas-kinetic cross section a k plays for the mechanical 
collisions, a can be considerably larger than a k , if W(r) is still large 
for great values of r; if, on the other hand, W(r) decreases rapidly with 
increasing r, the effective cross section can become much smaller than 
the kinetic cross section. This means only that not every kinetic 
collision produces the reaction under consideration, or that the yield 
of the collisions is below 100 % — it does not pretend that a molecule 
actually approaches the excited atom in a quenching collision to a 
distance smaller than the gas-kinetic radius. 

In determining the probability W(r) of an energy transfer from 
an excited atom in a collision process, a principle which was introduced 
by Franck in connection with problems of this type, and which has 
since been extensively applied by him and others, is of great im- 
portance : during the exceedingly short time of an electronic transition, 



92 MONATOMIC GASES AND VAPORS 

the location and the momentum of atomic nuclei cannot be altered 
appreciably because of the relatively large mass of the nuclei. There- 
fore, only a small part of the electronic excitation energy of an atom 
can be transferred directly into kinetic energy of the colliding particles. 
Either the excited atom loses only a small fraction of its energy and 
is transferred by the collision into a closely neighboring quantum 
state, or, if the atom loses a large fraction or all of its excitation 
energy, this energy must be converted almost completely into some 
kind of excitation energy of the perturbing molecule. The nearer the 
energy of a quantum state of the latter is to the excitation energy of 
the former, the better is the "energy resonance" between the two, and 
the greater is the probability W(r) for large values of r. The energy 
resonance reaches a maximum if the two particles are of the same kind, 
one atom being transferred from the excited state to the ground state 
and the second atom from the ground state to the very same excited 
state. This process, however, cannot be observed directly (412b). 

Kallman and London have treated the interaction between an 
excited atom and another atom almost in resonance with the first 
applying the laws of quantum mechanics. If S is the difference be- 
tween the excitation energies of the two systems and if the corre- 
sponding transitions are allowed (dipole radiation), the effective cross 
section increases proportionally with S _2/3 . However, for very small 
values of 8, a does not increase infinitely but tends towards a limiting 
value, which depends mainly on the relative velocity of the two atoms; 
the higher the temperature, the smaller is a in the case of sharp 
energy resonance (707). 

36. Collision- Broadening. Flame Fluorescence. Increase in width 
of spectral lines with increasing gas pressure has been known for a 
long time and has been interpreted by H. A. Lorentz as caused by 
"collision-damping"; according to the Fourier analysis, the lines 
become broader because the phase of the emitted wave is altered or the 
wave is completely interrupted every time the vibrating oscillator is 
perturbed by a collision. The equivalent of this explanation could not 
be found in Bohr's original theory, in which every individual emission 
process was instantaneous and strictly monochromatic, without any 
mention of phase relations. Collision-broadening was interpreted, 
according to the principle of correspondence either, by the shortening 
of the lifetime of the excited state, or it was ascribed to the pertur- 
bation of the excited level caused by the small distance between the 
colliding molecules ^molecular Stark effect) at the moment of emission. 
If the second assumption were correct, collision-broadening would 



COLLISION-BROADENING. FLAME FLUORESCENCE 



93 



become a pure configuration effect and would depend on temperature 
only insofar as due to the higher average kinetic energy, a close 
approach of two atoms occurs more frequently. The number of col- 
lisions per unit of time would be without importance ; if the configu- 
ration of the molecules at a high temperature could be suddenly 
' 'frozen, ' ' the width of the line would remain unchanged. This hypothe- 
sis was suggested by Einstein for an experimental test in the early 
days of Bohr's theory.andwas taken up again much later by Jablonski, 
after the introduction of "potential curves" for representing the 
energy relations between two atoms at variable distances (658,g8o, 
Ii8ia,i8i4,ig25). 

In Figure 36, the abscissa is the distance r between two atoms : 
the ordinate is the potential energy 
U as far as it depends on the elec- 
tronic configuration within the atoms 
and on the interaction between them. ^ 
For r = oo, U is determined exclus- f 
ively by the electronic energy, which 
is assumed to be if both atoms 
are in their ground state, and E if 
one of the atoms is excited. For 
the present considerations, it is as- 
sumed that with decreasing distance 
only repulsion forces between the 
two atoms need to be taken into account 



Fig. 36. Potential curves for col- 
lision-broadening ( Jablonski) . 



apart from the weak 
Van der Waals forces, which cause a flat trough in the potential 
curves,, with its lowest point at a certain value of r = r*. For distances 
smaller than r*, the slope of the potential curves becomes rapidly 
steeper, because of the strong repulsive forces. According to Franck's 
principle, an emission process can be due only to vertical transition 
(such as a, b, and c) between points of the upper curve and points of 
the lower curve. Since the two curves are not strictly parallel, the 
quantum hv which corresponds to such a transition has a different 
value from the quantum hv emitted at r = <». The superposition of 
many processes of this kind causes a broadening of the spectral line, 
which, in general, will be , asymmetrical. However, this type of 
broadening of spectral lines becomes important only at relatively 
high gas pressures; at the low pressures which generally prevail in 
experiments on resonance radiation, the broadened lines remain 
almost completely symmetrical and this effect must be due to another 
collision-damping theory, according to which the number of collisions 



94 MONATOMIC GASES AND VAPORS 

during the lifetime of the excited state determines the width of the 
line, while it is of no importance whether the emission is quenched 
or only changed in phase by a collision (goo, 901,1814). 

The greatest part of the investigations on collision-broadening 
deals with absorption processes and therefore, is not within the scope 
of this book. Even the broadening of emission lines excited by reso- 
nance has, in general, been determined by the change of absorbability 
of the line in a cell containing the same vapor as the resonance lamp. 
By this method, it could be shown that the mercury resonance line is 
broadened by the same amount whether the number of collisions in a 
mixture of mercury vapor and a foreign gas is increased by an increase 
of temperature at constant density or by an increase of pressure at 
constant temperature (1181a). Furthermore, it has been demonstrated 
that as long as the number of collisions is the same gases with a strong 
quenching action broaden the lines no more than other gases. The 
broadening effect of helium and hydrogen on mercury vapor or of 
argon and nitrogen on sodium vapor are respectively equal, though 
the rare gases have a very small, the others a very strong quenching 
efficiency. By means of fluorometric measurements, Duschinsky 
proved that the broadening of the resonance lines by rare gases is not 
caused by a shortening of the life of the excited states without simul- 
taneous quenching. If nitrogen or helium were added to sodium vapor 
in such quantities that their respective vapor pressure produced the 
same amount of collision-broadening of the D-lines, the duration of the 
resonance emission was reduced by nitrogen to about one-half, with the 
corresponding decrease of fluorescence intensity ; the fluorescence was 
neither quenched appreciably, nor was the lifetime t shortened to a 
measurable extent by the addition of helium. Hamos obtained the 
same result in a more indirect way, by showing that the quenching 
efficiency of nitrogen on the resonance radiation of sodium was not 
changed by the addition of helium. If the lifetime of the excited atoms 
were shortened by the action of the rare gas without simultaneous 
quenching, the quenching efficiency of nitrogen should be diminished 
as well according to the Stern-Volmer Equation (23) (326,569). 

Thus, collision-broadening by rare gases is not due to induced 
radiating transitions causing a shortening of lifetime of the excited 
state. If, on the other hand, the atom radiates spontaneously at the 
moment of collision, the frequency of the radiation will be noticeably 
a'tered, according to the potential-curve diagram of Figure 36; the 
consequence must be the appearance of an emission band in the vi- 
cinity of the normal atomic line. Oldenberg has actually observed a 



COLLISION-BROADENING. FLAME FLUORESCENCE 95 

narrow diffuse band on the long-wavelength side of the mercury 
resonance line which was produced, apart from the resonance line 
itself, by irradiating a mixture of mercury vapor and inert gases with 
the radiation of a mercury lamp (1168). Simultaneously, bands with 
a well-defined structure occurred in the fluorescence spectrum; they 
were ascribed by Oldenberg to excited rare gas-mercury molecules and 
are treated in a later chapter (Section 75). It is to be assumed that the 
transition probability between the upper and the lower potential 
curves of Figure 36 is altered and probably increased for small values 
of r. This would shorten the lifetime of the excited mercury atoms 
participating in these perturbed emission processes. However, their 
number is relatively small and neither the average lifetime of the 
other atoms (which is obtained by the fluorometric measurement) nor 
the width of the line emitted by them would be influenced by such 
processes. 

By an increase of the pressure of the fluorescent vapor itself, the 
resonance lines are broadened much more than by the addition of a 
foreign gas, if the number of kinetic collisions is the same in both cases. 
The effective cross sections are much larger when the energy resonance 
between the colliding atoms is complete (1184,1478,1479,1480). 

If the absorption line of a vapor is broadened by collisions, the 
resonance line has the same width in the fluorescence spectrum as the 
absorption line, even when the exciting line is narrow (1183). 

The intensity of the resonance fluorescence of a vapor is frequently 
increased when the absorption line is broadened by collisions. The 
exciting line in the spectrum of the primary light source has nearly 
always a greater width than the absorption line of the resonance lamp 
and, therefore, a larger fraction of the incident energy is absorbed, if 
the width of this absorption line is increased. The intensity of the 
resonance fluorescence of mercury or sodium vapor may become sev- 
eral times stronger by addition of helium of 100 mm. (The intensity 
decreases, however, under otherwise equal conditions, if the narrow 
line of a resonance lamp is used for excitation) . Even if the foreign gas 
quenches the resonance radiation considerably, this effect can be 
overcompensated by the broadening of the line, especially if the line 
is more or less self -re versed in the primary radiation. According to 
Badger, the mercury resonance radiation is almost completely 
quenched by a few cm of nitrogen if a resonance lamp is used for 
excitation, while under excitation by a mercury arc the fluorescence 
intensity is almost independent of the nitrogen pressure, up to 760 mm 
(j5.j-r67.rf67). 



96 



MONATOMIC GASES AND VAPORS 



Badger ascribes to the same cause the phenomenon which Nichols 
and Howes called "flame fluorescence" and which they observed at 
first only in flames colored by the evaporation of a thallium salt. If a 
Bunsen flame is supplied with a metal vapor (Tl, Mg, Ag ; also with, 
less efficiency, Cd, Hg, Na) and if it is irradiated with light containing 
the resonance line of the metal, the resonance line and possibly, by 




Fig. 37. Transfer of Hg-hyperfine-structure component 

- 25.4 by collisions of excited Hg-atoms with He-atoms 

(Mrozowski) . 

1. No helium present. 2. complete hyperfine 

structure of Hg-line 2537 A. 3. with 0.7 mm He. 



stepwise excitation, some of the other series lines are re-emitted by 
the flame, often with considerable intensity. Special experiments 
showed that neither the temperature nor any other specific conditions 
prevailing in the flame were responsible for this phenomenon (35, 
gyy,in8). 

37. Transfer of the Excited Atom into Adjacent Quantum States. 
The smaller the energy difference between two electronic states of an 
atom, the greater becomes the probability that a transfer of the atom 
from one state to the other will be produced by a collision. The con- 
dition of smallest energy difference is fulfilled for the hi .s.-levels of 
the state 6 3 P 1 of mercury. Mrozowski observed that if the mercury 
fluorescence is excited by the isolated component — 25.4 (see Figure 
19) of the resonance line 2537A in the presence of a foreign gas, the 
other components of the hyperfine structure belonging to the isotopes 
Hg 199 and Hg 201 are emitted together with the exciting line. The 
components belonging to the even isotopes are missing in the fluo- 
rescence spectrum (Figure 37). The addition of 0.1 mm helium or 



TRANSFER INTO ADJACENT STATES 97 

nitrogen is sufficient to produce this effect. On increasing the mercury 
pressure itself, however, all h.f.s. -components appear in the fluo- 
rescence spectrum, even if a single component is used for the excitation. 
In this case it is not the primarily excited atom which is transferred 
into a neighboring quantum state by a collision ; the excitation energy 
is transferred to another atom, which is in almost complete energy 
resonance with the first one (the energy difference being of the order 
of 2-10~ 5 eV): it is thus an instance of "sensitized fluorescence" (see 
Section 43). According to Mrozowski, the half-pressure p* is about 0.1 
mm for this energy transfer ; because of the smaller atomic velocities, 
the frequency of collisions is about ten times smaller than in the case 
of energy transfer due to collisions with helium which has been 
mentioned above. Mrozowski's statements are not sufficient for more 
quantitative conclusions with respect to the increase of the effective 
cross sections (J072). 

Decreasing the energy differences between the mercury h.f.s.- 
levels still further by the action of a magnetic field, Buhl finds that the 
effective cross section for the energy transfer from one mercury isotope 
to another can be more than one thousand times larger than the gas- 
kinetic cross section (185). 

The energy difference between the two 3P-levels of sodium 
(3 2 P 1/2 and 3 2 P 3/2 ) is equivalent to about 2- 10~ 3 eV. If the exciting 
light contains only one of the D-lines, the other D-line appears also in 
the emission spectrum if hydrogen, nitrogen, or a rare gas is added to 
the sodium vapor in the resonance lamp. If the partial pressure of the 
foreign gas is increased to a few mm, the relative intensity of the D- 
lines tends towards the normal ratio 1 : 2, corresponding to the statisti- 
cal weights of the two 2 P-levels, irrespectively of whether B 1 or D 2 is 
used for excitation ; because of the smallness of the energy difference, 
transitions in both directions are almost equally probable even at a 
temperature of 100° C. However, the half-pressure of 3 mm of argon is 
> 10 times larger than that obtained for transitions between the 
h.f.s. -levels of mercury, corresponding to the considerably larger 
energy difference which must be bridged. Increase of the sodium vapor 
pressure itself has, again, a particularly strong effect: at a sodium 
vapor pressure of 2- 10~ 3 mm, transitions between the two 2 P-levels 
are as frequently induced by collisions as at an argon pressure of 0.6 
mm. The effective cross section is about 200 times larger in the first 
case than in the second (944,1895,1911). 

The appearance of the violet line 4058A in the fluorescence spec- 
trum of lead vapor (see Section 15) can also be explained only by a 



98 MONATOMIC GASES AND VAPORS 

transfer of atoms from the excited state 3 PJ to 3 Pg, since a direct ex- 
citing transition from the ground state 3 P to 3 P% is strictly forbidden 
(4/ 7^ for / = 0). The energy difference between the two 3 P°-states 
is only 4- 10 -2 eV, and it is probable that the lead vapor pressure in 
Terenin's experiment was sufficiently high for the occurence of trans- 
ferring collisions (1631,1849). 

According to Paschen, the resonance doublet of orthohelium has 
its normal intensity ratio in the fluorescence spectrum, although the 
short-wavelength component, 10829.11 A, is much weaker in the 
primary radiation and is less absorbed by the metastable helium atoms 
in the fluorescence chamber. Also, in this instance, the equilibrium 
was re-established by collisions between the excited and the normal 
helium atoms; the helium pressure was of the order of magnitude 
of 0.1 mm in Paschen's experiments, (ngj). 

If cesium vapor is excited by the absorption of the line 3989A 
(8 2 P 1/2 <- 6 2 S 1/2 ) in the presence of a few mm of helium, not only the 
lines which are excited directly or in steps (compare Section 16), but 
numerous further lines are re-emitted, among them, also, the second 
doublet component originating from the state 8 2 P 3/2 . The emission of 
most of these lines is due to the transfer of excited atoms by collisions 
from the state 8 2 Pi /2 into the closely adjacent 8Z)-levels. The tran- 
sitions corresponding to the observed new lines are marked in Figure 
13 by thin lines; the thin dotted lines are, again, the transitions corre- 
sponding to spectral lines which are missing in the spectrograms only 
because of their long wavelengths. The lines originating from 8 2 5 1/2 
show relatively small intensities, owing to the greater energy differ- 
ence between this level and the state 8 2 Pi /2 — 0.043 eV as compared to 
0.01 eV for the transfer to the 8Z)-levels (125). 

The emission of the D-lines by sodium vapor, which is excited by 
absorption of the second doublet of the main series, has been explained 
by Bohr by a spontaneous stepwise return into the ground state (see 
Section 16). Franck assumed at first that the phenomenon was due, 
at least partially, to a transfer by collisions. This interpretation 
appeared admissible, because in Strutt's original experiment the 
sodium vapor pressure was sufficiently high, and because in the later 
repetitions of the experiment at low vapor pressure, the effect was 
appreciably increased by the addition of argon of a few mm. The 
D-lines emitted under these conditions are not noticeably weakened 
by passing through a thick layer of sodium vapor, while the resonance 
radiation excited in the same tube by irradiation with the D-lines is 
completely absorbed by such a cell. The greater line width in the first 



TRANSFER INTO ADJACENT STATES 99 

case was ascribed by Franck to the Doppler effect resulting from the 
surplus energy which would be liberated by a collision transfer from 
4?P to S 2 P. The transfer of so much electronic energy (1.64 eV) into 
kinetic energy of the colliding particles is not compatible withFranck's 
principle. Berry and Rollefson supposed, therefore, that the collisions 
transfer the excited atoms from the state 4P to 4D with a surplus 
energy of only 0.14 eV, which still leaves to the atoms a velocity 
sufficient to explain the greater line width in the subsequent stepwise 
emission of the lines 4£» -> 3P and the D-lines (3P -» 35) (g6). 

A relatively small energy difference separating the metastable 
state 6 3 P from the state 6 3 P 1 is characteristic of the mercury atom. 
If atoms which have been raised to 6 3 P X by absorption of the resonance 
line are subsequently transferred into the metastable state by col- 
lisions, the resonance radiation is quenched. The presence of metastable 
atoms in the vapor is proved by the appearance of the lines 4047 and 
2967 in the absorption spectrum (i88g)- 

It mercury vapor is irradiated with strong light containing the 
resonance line, the absorption of the line 4047A becomes noticeable 
at a partial nitrogen pressure of 0.1 mm and is very conspicuous at a 
pressure of 2 mm. At still higher pressures, the absorption line is 
assymetrically broadened. However, the strength of the absorption 
cannot be used as a quantitative measure for the number of atoms in 
the metastable state, since the absorption tends towards a limiting 
value which depends on the shape of the line in the transmitted 
radiation. 

The energy difference of 0.218 eV between 6 3 Pj and 6 3 P is so 
large that, at room temperature, only every 2,000th collision has the 
energy necessary to reverse the process. An admixture of a fraction of 
one per cent of quenching impurity is, therefore, sufficient to stop 
almost completely any return to the higher level. On the other hand, 
the energy of 4.7 eV separating the metastable state from the ground 
state is so large that the quenching transition to the ground state 
cannot be induced by a collision without some kind of energy reso- 
nance. Hence, the concentration of the metastable atoms can become 
rather large if such collisions are improbable. The equilibrium con- 
centration depends on the intensity of the primary radiation, on the 
probability of diffusion and of quenching collisions, on the return to 
6 3 P 1( and, as far as the odd isotopes are concerned, on the emission of 
the forbidden line 2656A {465,789). 

Even the energy difference of 0.218 eV is great enough to render 
the transfer from 6 3 P X to 6 3 P by a collision with an inert gas very 



100 MON ATOMIC GASES AND VAPORS 

improbable. However, the transfer can be produced with great effi- 
ciency if the excited mercury atoms collide with diatomic or poly- 
atomic molecules. This, again, is explained by resonance effects; the 
quantized nuclear vibrations of the molecules are assumed to take up 
the balance of the electronic energy of the mercury atom. The closer 
the energy of the first vibrational quantum of the colliding molecule 
to 0.218 eV, the better is the energy resonance and the larger should be 
the effective cross section for the "transferring collisions " The data 
which were published as proof for the validity of this hypothesis are 
listed in the first vertical column of Table 14 (Sect. 39). However, 
most of these "effective cross sections" were not obtained by measur- 
ing the equilibrium concentration of metastable atoms in the presence 
of the various gases, but by their quenching efficiency for the reso- 
nance radiation, which may also be due to genuine quenching, i.e., to 
transfer to the ground state (67, 317, 369,1924). Nitrogen, which ranks 
rather low in Table 14, is the gas which produces by far the greatest 
equilibrium concentration of metastable mercury atoms. At small 
nitrogen pressures, the yield is still increased by the addition of an 
inert gas which, in itself, is inactive, but which decreases the diffusion 
to the walls. In a specific case, the equilibrium concentration of the 
metastable atoms measured by the absorption of the line 4047A was 
reached at a nitrogen pressure of 2 mm; if neon of 12 mm was added, 
it occurred, under otherwise unaltered experimental conditions, at 
0.8 mm of nitrogen {465,789). 

If other gases are more efficient than nitrogen in transferring 
mercury atoms from the state 6 3 P X to 6 3 P , they must also have a 
much greater effiiciency in real quenching. This is proved for nitric 
oxide by the different influence which a rise in temperature produces 
in the quenching efficiency of this gas and of nitrogen. If a mercury 
resonance lamp, in which the fluorescence is almost completely 
suppressed by* nitrogen of sufficient pressure, is heated to 750° C, 
the intensity of the radiation is restored nearly to the value which it 
had in the absence of nitrogen. At this temperature, collisions causing 
the retransfer from 6 3 P to 6 3 P 1 are sufficiently frequent, while genuine 
quenching collisions practically do not occur. It cannot be assumed 
that the first part of the process (the transition 6 3 P 1 -> 6 3 P ) is 
suppressed at high temperatures : while at 750° C the mercury resonance 
radiation is as strong in the presence of nitrogen of 40 mm as without 
nitrogen, it is much more strongly quenched by an addition of hydro- 
gen in the first case than in the second {203,1167). By the intermediate 
transition into the metastable state the total lifetime of the excited 



TRANSFER INTO ADJACENT STATES 



101 



f, 5 



NO 135) 
0.2188V 



H.O 



atoms is lengthened and thus they have a greater probability of being 
quenched by a collision with a hydrogen molecule. (This observation 
shows that the metastable mercury* atoms, also, lose their electronic 
energy by collisions with hydrogen molecules. According to E. Meyer, 
the probability of such a pro- 
cess is practically the same 
for mercury atoms in the 
states &>P 1 zn&6 3 P ) (1022a). 

Nitric oxide of 6 mm 
quenches the mercury reson- 
ance radiation at room tem- 
perature to 15% of its value 
in the absence of a quenching 
gas. At 650° C the intensity 
increases only to 25 % of this 
value ; in this case the major 
part of the loss is caused by 
genuine quenching and can- 
not be reversed by an incre- 
ase of temperature. It is true 
that a relatively small qu- 
enching efficiency can be 
sufficient for producing this 
result because of the long 
lifetime of the state 6 3 P , and 
thus the direct quenching of 
the atoms in the state 6 3 P 1 
may be negligible. 

Nevertheless, the "resonance curve" which has been derived 
from the figures of Table 14 still has a somewhat hypothetical charac- 
ter. The ordinate in this curve (Figure 38) represents the quenching 
cross section of each gas and the abscissa the difference between the 
lowest vibrational energy of the molecules and 0.218 eV. The peak 
of the curve corresponds to the gas with the best energy resonance. 
The two vertical lines at the center of the figure indicate the "un- 
sharpness of energy" caused by the thermal agitation. For a quantita- 
tively satisfactory treatment of the problem, the quenching of the 
resonance radiation, its dependence on temperature, and the number 
of metastable atoms in equilibrium should be known fox every gas as 
a function of its pressure. In not a single case are all these data 
available. (Compare Section 40). 





14 



18 



az 



26 



30 xio'ev 



Fig. 38. "Resonarice curve" for the 

quenching of Hg-resonance radiation 

by various gases (Bates). 



102 MONATOMIC GASES AND VAPORS 

Interaction with mercury atoms in the ground state seems also 
to induce the transition of excited mercury atoms into the metastable 
state with great efficiency. An increase of the mercury vapor pressure 
from 10~ 3 to 1 mm causes a decrease of the fluorescence yield by 50 %. 
It is not yet possible to determine whether metastable atoms in the 
state 6 3 P are directly produced in this process, or whether inter- 
mediate Hg 2 -molecules are formed (compare Section 76). At any rate, 
the metastable modification originating from a collision between an 
excited and an unexcited mercury atom has an energy not below 4.65 
eV and is able to retain it through a great number of further collisions 
with mercury atoms (1182) . 

The energy-level scheme of cadmium is completely analogous to 
that of mercury, but the distance between the levels 5 3 P t and 5 3 P is 
equivalent to only 0.07 eV. Transitions between the two states are, 
therefore, almost equally probable in both directions, even at the 
lowest temperatures of observation (about 250° C), so that the con- 
centration of metastable atoms never becomes very large. Because of 
their small number, it is difficult to prove their presence by the ob- 
servation of the characteristic new absorption lines. However, Bender 
was able to demonstrate the transfer 5 3 Pj -+ 5 3 P due to collisions 
with N 2 or CO-molecules by the appearance of new lines in the fluo- 
rescence spectrum which was caused by stepwise excitation. In con- 
tradistinction to the similar phenomenon in mercury vapor, the 
transfer cannot be ascribed to resonance with the vibrational frequen- 
cies of the molecules, and it is to be expected that it would be produced 
with not much smaller efficiency by collisions with monatomic gases 
[66,91). 

38. Effect of Collisions on the Polarization of Resonance Radiation. 
The considerations which were applied in the last section to the trans- 
fer between closely neighboring levels retain their validity for the 
effect of collisions on the polarization of resonance radiation. The 
complete or partial polarization of radiation is caused by the exclusive 
or preferential population of some of the magnetic levels of an electro- 
nic state. If, by collisions, the relative -population of the several mag- 
netic levels is brought closer to the statistical equilibrium, the polari- 
zation decreases and is eventually destroyed. Since the energy dif- 
ference between the magnetic levels is proportional to the field 
strength, the depolarization by collisions is expected to become 
noticeable at very low pressures in weak or vanishing magnetic fields. 

Figure 39 shows the degree of polarization of the mercury reso- 
nance radiation as a function of the pressure of various foreign gases, 



COLLISIONS AND POLARIZATION OF RESONANCE RADIATION 103 



after Keussler's measurements. Similar curves were obtained by 
Hanle for the D-line resonance in sodium vapor excited by circularly 
polarized light. The main difference between the two sets of curves 
consists in the order of magnitude of the "half pressures" p* at which 
the degree of polarization drops to one-half of its maximum value, p* 
is considerably larger for sodium than for mercury, in accordance 
with the shorter lifetime of the excited state of sodium. With an inert 
gas, which is the most likely to give comparable results in both vapors, 
p* is 0.77 mm for mercury and 3 mm for sodium. For the singlet 
resonance line of cadmium, the value of p* is even 10 mm. The pre- 

80 



-40 





°-H 2 


L o z 


x^5 

1 


• 


N 2 

i 



1.0 2.0 

Pressure in mm 



3.0 



Fig. 39. Polarization of Hg-resonance radiation as 
a function of the pressure of foreign gases (Keussler) 

sence of 1 .5 mm of nitrogen, by which most of the mercury atoms are 
transferred after absorption of the resonance line into the metastable 
state, has practically no influence upon the polarization of the lines 
originating from the state 7 3 S lt which is reached by stepwise excitation ; 
as already mentioned, the lifetime of this state is only of the order of 
5-10- 9 sec {571,574,728,729,773). 

The "depolarizing cross section" of the molecules of various 
gases cannot be derived directly from curves like those of Figure 39, 
because the quenching action of a foreign gas may partially compen- 
sate its depolarizing action. For this reason, hydrogen or oxygen, 
which are good quenchers for the mercury resonance radiation, 
decrease its polarization much less than the inert gases at the same 
pressure. Measuring the quenching and the depolarization of the 
mercury resonance radiation by hydrogen or deuterium separately, 
Suppe has calculated the genuine depolarizing efficiency of these 
gases, which is compared in Figure 40 with their apparent depolarizing 
efficiency {773,159 s )- 

The competition between depolarizing and quenching action be- 



104 



MONATOMIC GASES AND VAPORS 



60 



40 



20 



\ 

^ — * 



comes particularly evident if the decrease in polarization is brought 
about independently of the collisions by a magnetic field of appropri- 
ate orientation. The magnitude of both effects (quenching and de- 

^_^ polarization) is determined by the 

lifetime of the excited state. If the 
lifetime is shortened by the ad- 
dition of hydrogen to excited 
mercury vapor, not only is the in- 
tensity of the emitted radiation 
reduced but, simultaneously, the 
depolarization and the rotation 
of the plane of polarization by a 
longitudinal magnetic field de- 
crease [i22g). 

A magnetic field parallel to 
the direction of the primary radi- 
ation is not able to compensate 
the depolarizing action of collisions 
with the molecules of a foreign 
gas. Beyond a field strength of 200 
gauss, the curves of Figure 41 run 
almost parallel to the abscissa ; the 
probability of the transfer into another magnetic level is very little 
influenced by the exact value of the energy difference between these 
levels, which remains small for all magnetics fields in this series of 
experiments. The slope of the first part of the curves, for H below 
200 gauss, can be attributed to the the fact that depolarization, 
which is caused by the interaction with other sodium atoms, is compen- 
sated to a much higher degree by the magnetic field. 

This depolarization by interaction with atoms of the same kind is, 
again, a resonance effect, with the very large effective cross sections 
which are characteristic of atoms with good energy resonance. If, for 
instance, an excited sodium atom passes from the magnetic level 
m — — \ of the state 3 2 P 1/2 to the level m — + \ of the ground 
state, another atom may be raised from the level m = — \ of the 
ground state to the level m = — | of the excited state. In weak 
magnetic fields, the energy difference between these transitions be- 
comes exceedingly small and the energy resonance is correspondingly 
sharp {1142,1480). 

The strong depolarizing effect of atoms of the same kind at even 
rather low vapor pressures on the resonance radiation of Hg and Na 



mm H 2 or D 2 

Fig. 40. Apparent (a) and real (b) 
depolarization of Hg-resonance ra- 
diation by hydrogen and deuterium 
(Suppe). 



COLLISIONS AND POLARIZATION OF RESONANCE RADIATION 105 











a 
p 










% 






* 






— u 




c 














- A 


(/ 




I9^ a ~ a 




"» " 


1 


V 


- B 


"/ 




I 


1 


1 





has actually been realized from the beginning. In later quantitative 
investigations, however, a few discrepancies have not yet been 
elucidated. Ellett et al. find no appreciable influence of the vapor 
pressure on the polarization of the 
D-line fluorescence in sodium vapor 
saturated at temperatures below 
135° C. They obtain the same degree 
of polarization of 16.4% in the 
absence of a magnetic field, no matter 
whether the observations are made 
at 135° C (1.6- 10-« mm) or at 85° C 
(10 -8 mm). Datta, on the other 
hand, reports a continuous and in- 
creasingly steep rise of the degree 
of polarization with decreasing 
vapor pressure down to 115° C, and 
Hanle confirms this result in his 
experiments with circularly polarized 
light. It can hardly be assumed that 
these discrepancies are to be ex- 
plained by measuring errors alone 

{259,35i,356,467,573)- 

Figure 42' shows the degree of 

polarization of mercury resonance 

radiation excited by plane-polarized 

light as a function of the mercury 

vapor pressure, and Figure 43, the polarization of the D-lines excited 

by circularly polarized light as a function of the sodium vapor pressure. 

The scales of the abscissas of the 
two figures prove that, in contra- 
distinction to the effect of pertur- 
bations by foreign gases, the sodium 
lines are much more sensitive than 
the mercury line to increasing vapor 
pressure. According to wave me- 
chanics, the interaction between 
atoms of the same kind depends not 
only on the sharpness of resonance 

Fig. 42. Polarization of Hg-reso- but als ° ° n the di P ole m °ment °* 

nance radiation as a function of the oscillations which correspond to 

Hg-vapor pressure (Keussler). a transition between two electronic 
Pringsheim 4 



80 



60 



40 



20 



200 400 600 

Field strength in gauss 

Fig. 41. Depolarization of circu- 
larly polarized Na-resonance 
radiation by He-Ne mixture at 
various magnetic field strengths 
(Hanle). 

Pressure of He-Ne 
a: 0.0 mm d: 1.2 mm 

6: 0.2 e: 2.3 

c: 0.4 /: 3.7 



100 








i i i 

H«?900 gauss 


60 
40 
20 


















kJ1 = 


500 < 


jauss 










H * 


o ■"- 








i 


i 


j 








3 2 


4 
ry pr 


6 
essurc 


8 

> in m 


l( 
mX 


30 
10* 





106 



MONATOMIC GASES AND VAPORS 



states. The dipole moment corresponding to the mercury intercombi- 
nation line, with its smaller transition probability, is weaker and, 
therefore, an energy transfer by resonance becomes less probable. 
The intercombination resonance line of cadmium, with its still longer 
lifetime, has attained its highest degree of polarization at a saturation 
temperature above 170° C (about 2- 10~ 5 mm),* while the polarization 

of the singlet resonance line of 
cadmium increases continuously 
down to pressures below 10~* mm. 
The second doublet of the principal 
series of sodium, which has a much 
smaller intensity in the sodium 
absorption spectrum and a much 
smaller oscillator strength than 
the D-lines, shows a measurable 
decrease of its polarization only if 
the vapor pressure exceeds 2.4- 10~ 5 
mm (354). 

The polarization of the mer- 
cury line 4358A is expected to be 
negative and its intensity weak 
(compare Section 27) if both lines 
serving for the stepwise exci- 
tation (2537 and 4358A) are plane 



80 



60 



40 



20 













^ 






f 


i 




a 


V 




b 


c ■ 

I 






-V 








< 


>■ — 













10"' 



8X10 



2 4 6 

No-pressure in mm 

Fig. 43. Circular polarization of 
Na-resonance radiation as a function 
of Na-vapor pressure at various 
magnetic field strengths (Hanle). 

a: gauss d: 180 gauss 

6: 60 e: 300 

c: 120 /: 600 



polarized perpendicularly to the direction of observation, and if no 
perturbations occur during the process. Under these conditions the 
even isotopes cannot reach the excited state 7 3 S 1 in two successive 
37-transitions, since m would have to remain zero and A] would be 
zero in the second step from S 3 ^ to 7^^^ (see selection rules for m in 
Section 13). Thus, only the odd isotopes for which m = ± V 2 and 
± 3 / 2 in the ground state would participate in the emission of the 
blue line. If, however, all magnetic levels of the state 6^ are 
populated in consequence of the interaction between the excited atoms 
and other mercury atoms (or, in other words, if the resonance line 
itself is depolarized by the vapor pressure of the mercury), the line 
4358A should show a positive polarization of 26.9 %. The resonance line 
is already appreciably depolarized in saturated mercury vapor at 0° C 
(2-10 -4 mm) (see Figure 42) and, accordingly, the degree of polari- 
zation of the line 4358A is + 20 % under these conditions. It increases 

* At 210° C (about 3- 10 -4 mm) the degree of polarization of this cadmium 
line is about one-half of the maximum value. 



COLLISIONS AND POLARIZATION OF RESONANCE RADIATION 107 



80 



60 



40 



20 



i 

__ — *" 5 ' 
•^- - " 
^-^' — e 



800 



to -f 26% if the temperature is raised to 18° C and the vapor pressure 
to 10~ 3 mm. This exceptional behavior (the enhancement of the 
polarization of fluorescence by increasing vapor pressure) is due to the 
fact that even at the higher pressures the number of atoms in the state 
6 3 P 1 is negligibly small. Therefore, the state 7 3 S X from which the line 
4358A originates is not perturbed by resonance effects, since transitions 
between 7 3 S X and the ground state S^ are not to be considered either. 
An increase of the vapor pressure thus destroys the polarization of the 
resonance line by resonance in- 
teraction, but leaves the polari- 
zation of the line 4358A unaf- 
ected (72g). 

The points of Figure 43 are 
replotted in a different way in 
Figure 44. The curves of Figure 
44 show that the depolarization 
caused by the interaction with 
atoms of the same kind is coun- 
teracted to a large extent by mag- 
netic fields. The higher the vapor 
pressure, the stronger the mag- 
netic fields that must be applied. 
The separation of the magnetic 
levels is greater in a strong field ; 
therefore, the resonance between 
the transitions from these various 
levels to the ground state becomes 
less and less sharp and, corres- 
ponding to the theory developed 
by Kallman and London (Section 
35), the effective radius for the depolarizing perturbations becomes 
smaller. Hanle has tested this theory quantitatively by measuring 
the circular polarization of the D-line fluorescence of sodium vapor 
in magnetic fields of increasing strength and, on the whole, he found 
a good agreement between theory and experiments. The effective 
cross section was approximately proportional to S~ 2/3 [S = h(v — v )], 
even at smaller values of 8 than predicted by the theory (577). 

According to Buhl, the depolarizing cross section of mercury 
atoms for the mercury resonance radiation does not follow Kallmann's 
and London's law but is proportional to S -2 . Buhl interprets his result 
by the assumption that, in this case, the coupling between the reso- 
Pringsheim 4* 



200 400 600 
Field strength in gauss 



Fig. 44. Circular polarization of Na- 
resonance radiation as a function 
of the magnetic field strength at 
various vapor pressures (Hanle). 

a: 115°, 2-10-' mm 
b: 120°, 5-10- 7 
c: 135°, 1.6- lO- 6 
d: 165°, 8-I0- 6 
e: 195°, 5-10- 5 



108 



MONATOMIC GASES AND VAPORS 



nators is due mainly to the electromagnetic field of the radiation and 
not to the dipole moment of the resonators {185). 

From Hanle's experiments, the effective depolarizing radius of 
sodium atoms for the D-line fluorescence was calculated to be IQr* cm 
or about one thousand times as large as the gas-kinetic radius. The 
effective depolarizing radius of mercury atoms for the Hg-resonance 
line is only 0.75- 10 -6 cm or 50 times the gas-kinetic radius. However, 
even if the energy differences between the magnetic levels of the 
excited atoms become relatively large in strong magnetic fields, the 
depolarization caused by the interaction with atoms of the same kind 



100 



80 



60 



40 



20 











- • 










1 vC- 










<^^-^- 












v 2 ■ 


-\\ 






--^t; 


■-1^-— 


"---. 


■ - __ 




-41 


- 


>. 


^^•j"-^- 




.CO 






s^ 


3^li 


1 


1 


1 










1 


Air 


1 


-» 2 



12 3 4 

Pressure in mm 

Fig. 45. Quenching of Hg- (continuous lines) and Na- 

resonance (broken lines) radiation by various gases 

(Mannkopf and Stuart). 

does not completely disappear; the curves of Figure 44 do not tend 
asymptotically toward the same limiting value. This has also been 
proved by Schuetz; in a field of 18,000 gauss he still obtained a 
noticeable depolarization of the mercury resonance line at a vapor 
pressure of 10~ 3 mm, and, using the Malinowski method, he proved 
that the a-components are still excited under experimental conditions 
(case I) under which the ^-components alone should be excited in 
the absence of perturbations {1478, 1479). 

39. Quenching of Resonance Radiation by Collisions. While in 
"transferring" collisions, which were dealt with in the foregoing 
sections, the main part of the electronic energy remains in the 
primarily excited atoms, genuine "quenching" collisions are character- 
ized by the complete loss of the excitation energy. (If both processes 
occur simultaneously, it is difficult to separate them). 

The quenching of the fluorescence of vapors by the addition of 



QUENCHING OF RESONANCE RADIATION BY COLLISIONS 



109 



foreign gases (atmospheric air, oxygen, chlorine, etc.) has been 
described by Wood in one of his first papers dealing with resonance 
radiation. The first systematic measurements on quenching were 
published by Stuart and by Mannkopf for the resonance radiation of 
sodium and of mercury, respectively (Figure 45) {976,1595). Zemanski 
has brought forward a number of objections to the lack of precision of 
these early observations. In the case of mercury, no distinction had 



^io„ 



2 - 



- 




/ C 6 H 6 




-/-- 


1 


1 


1 



Pressure in mm 

Fig. 46. Quenching of Na-resonance radiation by various gases 
(Norrish and Smith). 

been made between the transfer into the metastable level and genuine 
quenching. The possibility of an increase of intensity caused by the 
broadening of the absorption lines has already been mentioned. If, on 
the other hand, the exciting line is very narrow — for instance, if it is 
emitted by a resonance lamp — it is absorbed less if the absorption 
line is broadened; thus, the intensity of the fluorescence becomes 
weaker without any real quenching action by the foreign gas. According 
to Zemanski, the quenching of the mercury resonance by inert gases, 
shown in Figure 45, is due to this cause alone. To avoid these effects, 
the measurements must be limited to pressures of the quenching gases 
so low that the width of the lines is still essentially determined by the 
Doppler effect. Another possible source of error is a chemical reaction 
of the metal vapor with the foreign gas — for instance, of mercury 
with oxygen or of sodium with nitrogen — by which the pressure of the 
metal vapor can be altered in an uncontrollable manner (463). Because 



110 



MONATOMIC GASES AND VAPORS 



t^tv--^- 



of the latter effect, Mannkopf's and Hamos' values for the quenching 
of sodium resonance radiation are probably too high. Norrish and 
Smith took special precautions for avoiding this source of error (see 
Tables 19A and B). Some of their results are represented in Figure 46, 
in which the reciprocals of the fluorescence yield are plotted versus 
the pressure of the quenching gas as straight lines, thus proving the 
validity of the Stern-Volmer equation (ii47)- Finally, the 
quenching efficiency can be increased if the resonance radiation is 

"imprisoned" in a metal vapor of 
relatively high pressure; because 
of the longer lifetime of the ex- 
cited states, the probability of a 
quenching collision becomes larger. 
In spite of all these objections, 
Stuart's and Mannkopf's papers 
already contained most of the 
principal results, to which only 
some quantitative corrections had 
to be introduced afterwards*: (i) 
various foreign gases differ widely 
in their action on a given excited 
atom, and the same gas acts very 
differently on various excited 
atoms ; (2) if the quenching process 
is to be described by the Stern- 
Volmer equation, "effective" radii 
must be introduced instead of the 
gaskinetic radii. If, for instance, 
the quenching efficiency of oxygen was assumed to be 100% in 
Stuart's experiments, an effective radius had to be ascribed to the 
mercury atoms in the state 6 3 P t which was 3.3 times larger than the 
gas-kinetic radius. (According to more recent measurements, the 
effective radii seem to differ less from the kinetic radii in this parti- 
cular case.) 

Zemanski's own method for measuring the quenching of the 
mercury resonance radiation is claimed to avoid all the objection 




Fig. 47. Zemanski's apparatus for 

the determination of quenching 

cross sections. 

L: light source. R: resonance 

lamp. Q: cell containing Hg- 

vapor and quenching gas. Pj : 

photocell in position 1 . P 2 : 

photocell in position 2. S: 

screens. 



* It may be mentioned here that even more recent measurements cannot 
claim absolute quantitative reliability. Thus, the quenching cross section of 
hydrogen for the Cd resonance line 3261A is listed in two papers as 0.67 and 
3.54- 10 -16 cm 2 ; in both determinations the same method was used and no 
reason could be found to explain the discrepancy. (See Table 15). 



QUENCHING OF RESONANCE RADIATION BY COLLISIONS 



111 



mentioned above. It was later applied by Bates and Evans to a great 
number of quenching gases. In Figure 47, mercury vapor contained 
in a thin plane-parallel cell Q is excited by a parallel beam coming from 
another resonance lamp R. The intensity of the total radiation leaving 
Q in the direction of the primary beam is measured by means of 
a photoelectric cell P. In order to separate the resonance radiation 
emitted by Q from the. primary light, P is placed either immediately in 
front of Q (position P 2 ) or at so great a distance from Q that practi- 
cally only the parallel primary beam enters P (position P^). Increasing 
quantities of the quenching gas are successively admitted into Q. An 
exact mathematical treatment of the problem can be given. The 
effective cross sections obtained by this method are, in general, 
smaller than those given in the earlier papers. Zemanski's results are 
listed in Table 14 together with some data published by Bates and 
Evans (67,369,1924, J926). 

Table 14 
Quenching cross Sections of Various Gases for Mercury 
Resonance Radiation* 



Gas 


a in cm* • 10 1 ' 


Gas 


a in cm 2 • 10" 


Gas 


a in cm* • 10" 


H,0 


1.43 


H, 


8.6 


CH 4 


0.085 


D,0 


0.46 


D* 


11.9 


C 2 H 6 


0.6 


NH, 


4.2 


O* 


19.9** 


C 3 H 8 


2.26 


NO 


35.3 


He 


negligible 


C 4 H 10 


5.8-8 


co a 


3.54 


Ne 


0.325 


C 7Hl 6 


34 


N 2 


0.27 


A 


0.223 


C 2 H 4 
C 6 H„ 


48 
59.5 



* Many of the figures contained in this table are taken from Mitchell and 
Zemanski's Resonance Radiation and Excited Atoms; in some cases they deviate 
considerably from the figures published by the authors in their original papers. 
Mr. Zemanski was kind enough to inform me that the deviations are caused by 
corrections which he found necessary to introduce in his calculations. 

** It is difficult to understand why the value 59- 10 -16 cm 2 , derived from 
Mannkopf's curve, is so much larger. At the corresponding half-pressure of 2 , 
the broadening of the absorption line by collisions is still negligible. The values 
for the rare gases are taken from a paper by Olsen (nysa) . 

For comparison's sake, the gas-kinetic cross sections of normal 
mercury atoms may be mentioned : they are 1 1 • 10 -16 cm 2 in nitrogen 
and of the same order of magnitude (between 9 and 1 1 • 10~ 16 cm 2 ) in 
all other gases listed in the table. According to Samson, the diffusion 
coefficient of metastable mercury atoms in oxygen is between 15.1 and 
18.4- 10 -16 cm 2 — about as large as the quenching coefficient in oxygen 



112 



MONATOMIC GASES AND VAPORS 



80 



60 



— so that, in this case, the gas-kinetic and the quenching coefficients 
would seem to be practically identical. The size of mercury atoms in 
the metastable state, measured by their coefficient of diffusion in 
nitrogen, is also nearly the same as the size of normal mercury atoms 
derived from the kinetic theory of gases (1232,1408,1289,1791a).* 

Two independent determinations of the quenching of the mercury 
resonance radiation by H 2 and D 2 have been published; it is very 
striking that both papers reproduce curves plotting the fluorescence 

|00 intensity versus the gas pressure 

which coincide exactly for hy- 
drogen and deuterium. Since the 
numbers of kinetic collisions are 
inversely proportional to the square 
roots of the molecular masses, the 
effective quenching cross sections 
of H 2 and D 2 derived from the 
curve of Figure 48 are directly 
proportional to these square roots. 
As a matter of fact, the values 
given in Table 14 for D 2 and H 2 
correspond to the ratio 11.9/8.6 = 
1.4 = -y/2- Thus, the smaller num- 
ber of collisions is exactly com- 
pensated by the smaller velocities 
of the molecules or by the longer 
duration of the individual collisi- 
on. While, in general, a law of 
this type governs the interaction 
of particles in nuclear physics, this 
is the only case where it has been found to be valid for the interaction 
between excited atoms and quenching molecules (369,1598). 

Even for the quenching of the corresponding resonance line of 
cadmium 32 16A by D 2 and H 2 , the ratio of the cross sections is quite 
different, about 1 / 2 insteadof -\fi. (The second pair of values mentioned 
in Table 15 even yields a ratio below 1 / 3 ). The quenching cross sections 
of other gases and vapors for the cadmium resonance line are collected 
in Table 15. As mentioned, some of the values published by different 
investigators do not agree very satisfactorily. The results marked 

* From measurements of the diffusion in mercury vapor Couliette derived 
an effective cross section of metastable Hg (6 3 P ) which was 1.5 times as large 
as that of normal mercury atoms \Phys. Rev. 32, 636 (1928)]. 



O 40 



20 



^^- 



2 4 6 

Pressure in mm 

Fig. 48. Quenching of Hg-resonance 
radiation by H 3 (closed circle) and 
D 2 (open circle) (Suppe). 



QUENCHING OF RESONANCE RADIATION BY COLLISIONS 1 13 

with one asterisk seem to be the more reliable ones (66, g 1,943,1 561) . 

Table 15 

Quenching Cross Sections of Various Gases and Vapors for 

the Cd Resonance Line 3261A 



Gas 


a 10" 


Gas 


a -10" 


Gas 


a 10" 


H 2 


3.54* (0.67**) 


CH 4 


0.012** 


C 2 H 4 


24.9* 


1>i 


1.80* (0.19**) 


C 2 H„ 


0.024** 


C 3 H 6 


29.1* 


CO 


0.14** 


C 3 H 8 


0.012* 


C 4 H 8 (1) 


35.2* 


HH 3 


0.052* (0.041**) 


C 4 H 10 


0.46* 


C 4 H 8 (2) 


30.6* 


Nz 


0.021** 


C 6 H 6 


28.4* 


C 2 H 2 


27* 



* After Steacy and Leroy (1561). 
** After Lipson. and Mitchell {943). 

Winans has developed a method for investigating the quenching 
of atomic fluorescence by foreign gases, which provides the possibility 
of observing the quenching cross sections at different relative velocities 
of the colliding molecules. The vapor of a metal halide — for instance, 
of sodium chloride — is dissociated by the absorption of ultraviolet 
light into an excited metal atom and a halide atom according to the 
equation : 

NaCl + hv -* Na(3 8 P l/2 ) + CI + Ekin (26) 

If the frequency of the absorbed radiation corresponds to a quantum 
h v larger than the minimum energy needed for the dissociation, the 
surplus energy E^,, is distributed between the two separating atoms 
according to the law of the conservation of momentum. It is thus 
possible, within certain limits, to impart to the excited metal atoms 
any desired velocity larger than the velocity of thermal equilibrium 
(627, 781,800,1267 a, 1644,1848). (Processes of this kind are discussed 
in more detail in the following chapter, Section 73). 

The method has the advantage of avoiding most of the difficulties 
mentioned by Zemanski. Since the primary absorption occurs in the 
continuous band of the molecules, the absorption of the exciting light 
is not appreciably influenced by collision-broadening, even at con- 
siderable pressures of a quenching gas. On the other hand, as practi- 
cally no unexcited atoms of the metal are present in the observation 
chamber, reabsorption and imprisonment of the resonance radiation 
are out of the question. (However, if the quenching gas has an ab- 
sorption band in the spectral region of the exciting light or of the 
resonance radiation, adequate corrections must be introduced into 



114 



MONATOMIC GASES AND VAPORS 



the calculations). Finally, it is possible to investigate the quenching 
action of vapors which would react strongly with the metal vapor itself. 
Tables 16 and 19A list the values obtained by means of this 
method for the D-lines of sodium: a is the effective cross section 
calculated from the "half -pressure" p*, and v x the additional velocity 
of the excited atoms due to the surplus energy, according to Equation 
(26). Compared with the thermal velocities, v x is, in general, large and, 
therefore, the calculation of a can be appreciably simplified by 
neglecting the thermal velocities. Under this assumption, the number 
of collisions z is given by the equation : 

z = cnv-wix) (27) 

where x = v x ■\/m/2kT 

X 

y, (x) = (e-**/x) + (2 + l/x*)-Je-£ 2 d£ 



n is the number of quenching molecules per cm 3 and 
m is their mass 

Table 16 

Effective Quenching Cross Section of Various Gases for the Na 

Resonance Radiation as a Function of the Exciting Wavelength 

and the Molecular Velocity 



Wavelength in A 


2400 


2380 


2311 


2300 


2232 


2082 


2026 


1990 


v t in cm/sec • 10 -4 


0.7 


0.7 


1.3 


1.4 


1.7 


2.4 


2.6 


2.8 


Nitrogen a-10 18 
Iodine <r-10 16 


58.5 
75 


60 


40 


48 


28 


24.9 
12 


15 


38.2 

17 



The gas-kinetic cross sections of sodium in the gases mentioned 
in Tables 16, 18, and 19A lie between 31 and 41 • 10~ 16 cm 2 , for sodium 
in I 2 it is 50- 10 -16 . Thus, the quenching cross sections do not differ 
much from the gas-kinetic cross sections, with the exception of argon, 
for which the ratio between quenching and kinetic cross sections is 
about one-to-ten. But even for argon, a is not vanishingly small 
as has been assumed by Zemanski for the inert gases colliding with 
excited mercury atoms. With argon as the quenching gas, each sodium 
atom suffers a number of collisions before it is quenched, so that is has 
acquired the average thermal velocity when the quenching collision 
occurs; theiefoie, an influence of the exciting wavelength on a is 
neither to be expected nor is it observed. If molecular iodine is the 
quenching gas, a decreases continuously with increasing t^; only for 



QUENCHING OF RESONANCE RADIATION BY COLLISIONS 1 1 5 

the greatest value of v x does a show a slight increase again. The results 
obtained with nitrogen are similar, while the influence of Dj on a is 
rather doubtful with atomic iodine as quencher (8o3,i26yb,i268). 

Winans' method has the disadvantage that it is practically im- 
possible to extrapolate the quenching cross sections characteristic of 
the atoms with normal thermal velocities from values like those of 
Table 16 and, thus, to compare the results with those obtained by 
other methods. A very arbitrary extrapolation from the three points 
given in Table 16 for the quenching efficiency of nitrogen leads to 
a = 83- 10 -16 for v-, ~0. This value was obtained by Hamos for 
excited sodium atoms of thermal energy, but it is certainly much too 
high and disagrees widely with the value found by Norrish and Smith 
which must, at present, be considered to be the most reliable (compare 
Table 19A).* The quenching cross sections found by Norrish for the 
quenching of the sodium resonance radiation by hydrogen and carbon 
monoxide are also hardly consistent with those obtained by Winans' 
method. They are inserted for comparison in Table 19A; Table 19B 
lists the effective quenching cross sections of a number of organic 
compounds for the D-lines (569,1147). 

The quenching efficiency of hydrogen and nitrogen for the second 
doublet of the principal series of sodium (4*P -»■ 3 2 S) was found by 
Berry and Rollefson to be of the same order of magnitude as that for 
the D-lines (96). 

Prileshajewa measured the quenching of the green thallium line 
by various gases using Winans' method of excitation. Table 1 7 gives 
the relation between a and the nature of the quenching gas for 
excitation with the radiation of a zinc spark. The complete lack of 
quenching by hydrogen is particularly remarkable (1267b, 1268, 1644). 

Table 18 lists all examples for which the quenching cross section 
has been investigated as a function of the relative velocities of the 
colliding particles. It is not possible to find any connection with the 
various processes which are assumed to produce the quenching 
(compare the following section). 

It must be mentioned, however, that in several instances other 
authors disagree with Prileshajewa in regard to the quenching 
processes (1270). 

* On the other hand, the values of Tables 16 and 19A are in fairly good 
agreement with those obtained by other authors using the same method under 
similar conditions. Hamos' result, and also the earlier ones published by Stuart, 
are probably caused by the fact that the sodium vapor pressure in the observation 
vessel was lowered by the reaction of the metal with the quenching gas. Norrish 
took special precautions in order to avoid this source of error. 



116 



MONATOMIC GASES AND VAPORS 



Table 17 

Quenching of the Green Thallium Fluorescence 
by Various Foreign Gases 



Quenching gas 


p* in mm 


a ■ 10" cm* 


°l" k 


Quenching gas 


p* in mm 


a ■ 10" cm 1 


°l a k 


o 2 


20 


86 


1.67 


A 


300 


2.6 


0.07 


co 2 


35 


21 


0.56 ' 


H 2 


? 


0.01 


10 -2* 


N 2 


— 


11 


0.29 


h 


4.9 


17 


— 


H 2 Q 


100 


1.0 


0.39 


I 


30 


63 


— 










Til 


5 


50 


— 



40. Mechanism of Energy Transfer in Quenching Collisions. 

According to Franck's principle, the electronic energy of an excited 
atom cannot be transferred directly into kinetic energy of the colliding 
particles. If the excitation energy has to be taken over almost com- 
pletely as internal energy of the quenching molecules, these must have 
some sort of excited states which are in energy resonance with the 
primarily excited atom. The most direct process of this type occurs 
if the quenching atom has among its electronic levels one of nearly the 
same energy as the primarily excited atom. Under these conditions, 



Table 18 

Variation Aa of the Quenching Cross Section with Increasing 
Relative Velocities of the Colliding Particles 



Fluorescing 




Na 




Tl 


vapor 










Quenching 


Aa 


Quenching 


Aa 


Quenching 


gas 




process 




process 


H 2 


irregular 


reaction ? 





? 


N 2 


negative 


collision of the 
2d kind 





collision of the 
2d kind 


o 2 


— 


— 


negative 


reaction 


CO 


irregular 


collision of the 
2d kind 





collision of the 
2d kind 


co 2 


negative 


reaction 


positive 


reaction 


H a O 


— 


— 





collision of the 
2d kind 


Br 2 


negative 


reaction 


— 


— 


I* 


negative 


reaction 


negative 


reaction 


I (atomic) 


irregular 


collisions of the 
2d kind 


irregular 


collision of the 
2d kind 


Til 




~ 


positive 


collision of the 
2d kind 



ENERGY TRANSFER IN QUENCHING COLLISIONS 



117 



the second atom is able subsequently to emit its characteristic radi- 
ation as "sensitized fluorescence." This very important phenomenon 
is treated separately in the last part of this chapter. 

The hypothesis of energy resonance between electronic transitions 
and nuclear oscillations of diatomic molecules has proved its usefulness 
in the discussion of the induced transfer of excited mercury atoms into 
the metastable state. Several authors have tried to apply the same 
hypothesis to genuine quenching, assuming that the colliding molecule 
takes up a great number of oscillation quanta at once. Table 19A 
provides an example of this kind for the quenching of the sodium 
resonance radiation. A is the difference between the electronic energy 
of the atom and the vibrational energy of the molecule containing v 
quanta of oscillation. 

Using the figures of Table 19A, Kondratiev and Siskin plotted 
a "resonance curve" of the same type as the curve of Fig. 38; they 
obtained similar results for the quenching of the green thallium line. 
However, the authors themselves point out that the quenching cross 



Table 19A 

Effective Cross Sections for the Quenching of Sodium Resonance 

Radiation as a Function of the Energy Resonance 



Quenching gas 


N 2 


NO 


o* 


CO 


H, 


Number of oscillation 
quanta v 


8 


10 


12 


8 


4 


Oscillation energy in eV . . 


2.24 


2.18 


2.12 


2.03 


1.93 


A in eV 


0.08 


0.02 


-0.04 


-0.13 


-0.23 




a q in cm 2 -10 16 


24.9 


31.6 


52.2 


13.4 


15.7 


(The same after Norrish) . 


(14.5) 






(28) 


(7.4) 



Table 19B 

Effective Cross Sections for the Quenching of the Sodium 

Resonance Radiation by Hydrocarbons 



Saturated compounds 


CT-10" 


Nonsaturated compounds 


a -10" 


CH 4 


0.11 


C 2 H 4 


44 


C 2H 6 


0.17 


C 3 H 6 


52 


C 3 H 8 


0.2 


C 4 H 8 


58 


Cyclohexane 


0.4 


CeH 6 


75 


Iso-octane 


0.8 


Hexadiene 


76 



1 1 8 MONATOMIC GASES AND VAPORS 

section a = found for the quenching of the thallium fluorescence by 
hydrogen is in complete disagreement with the hypothesis, and they 
draw the conclusion that the interpretation of the curves as resonance 
curves cannot be upheld. Moreover, the transfer of electronic energy 
into nuclear vibrations of such great amplitudes would be in contra- 
diction to Franck's principle in no lesser degree than the direct transfer 
into translation energy of the molecules. Thus, other possible processes 
producing these quenching actions must be looked for (803) . 

The first instance in which at least the overall reaction of a 
quenching collision could be determined was the weakening of the 
mercury resonance radiation by hydrogen. Franck and Cario proved 
that if a mixture of mercury vapor and hydrogen is irradiated with the 
mercury resonance line, hydrogen molecules are dissociated. The 
formation of atomic hydrogen can be proved by the reduction of a 
metal oxide such as copper oxide or tungsten oxide, or, if oxygen is 
present in the vessel, by the formation of water. The rate of dissocia- 
tion can be followed by measuring the decrease in gas pressure, all 
newly formed water vapor being frozen out. If oxygen is present at too 
high a pressure the reaction is inhibited by the strong quenching 
action of oxygen itself. On the other hand, the rate of reaction becomes 
small at low hydrogen pressures and correspondingly low probabilities 
of a collision between a hydrogen molecule and a short-lived excited 
Hg( 3 P 1 )-atom. The curves representing the quenching of the mercury 
fluorescence and the hydrogen dissociation as functions of the hydro- 
gen pressure are exactly parallel : the number of quenching collisions 
is proportional with the number of dissociation processes and probably 
the latter occur with a yield of 100 %. The dependence of the reaction 
rate on the hydrogen pressure disappears almost completely if nitrogen 
is added to the gaseous mixture; under these conditions the excited 
mercury atoms, which by collisions with nitrogen molecules have been 
transferred to the metastable state 3 P , have a high probability of 
colliding during their long lifetime with hydrogen molecules even at 
low hydrogen pressures. Mercury atoms in the states 3 P X and 3 P 
seem to be about equally efficient in dissociating hydrogen molecules 
(202a, 301, 1022a). 

The most obvious interpretation of the mechanism of this typical 
sensitized photochemical reaction, which is represented by the 
equation : 

Hg(6'P x ) + H 2 -> Hg(6iS ) + H(1*S ) + H(1 2 S ) (28 ) 

must probably be discarded. From the theoretical viewpoint, it is 



ENERGY TRANSFER IN QUENCHING COLLISIONS 1 19 

prohibited by Wigner's law of the conservation of spin angular 
momentum, according to which the loss of electronic spin in the 
triplet-singlet transition of the Hg-atom must be compensated by a 
corresponding increase of spin in the other partners of the process. 
This question has been discussed at length by Laidler (857). 

Furthermore, the heat of dissociation of hydrogen is only 4.46 
eV, so that the relatively large energy of 0.4 eV must be transferred 
into kinetic energy of the colliding particles. Conditions are only 
slightly more favorable for deuterium, with a heat of dissociation 
equal to 4.54 eV. The cadmium resonance line 3261A is quenched by 
hydrogen almost as strongly as the mercury resonance radiation, 
although the excitation energy of the cadmium atom is only 3.78 eV 
and is thus insufficient for the process described by Equation (28). The 
appearance of HgH- and CdH-bands, respectively, in the fluorescence 
spectra (see Section 74) proves that these compounds are formed in the 
mixture of the metal vapors with hydrogen under the influence of the 
irradiation (91,92, 1562,1630). Thus, one must assume that the primary 
quenching process follows the equation : 

M* +H 2 -+MH 4-H (29) 

In the case of cadmium, the available energy is just sufficient for this 
process ; in the case of mercury, the surplus energy can be taken over 
by the' HgH-molecules as nuclear vibration and rotation energy. 
Beutler and Rabinowitch have shown that a high rotational energy 
results with great probability from this type of reaction if the metal 
has a high atomic weight (106). The concentration of the HgH- 
molecules remains small, however; because of their small heat of 
dissociation and their great vibrational energy, they dissociate almost 
instantaneously. 

If the fluorescence of zinc vapor is excited by the full radiation of 
a zinc arc, the intensity of the triplet lines is much more reduced in the 
stepwise-excited fluorescence spectrum by an addition of 0.02 mm of 
hydrogen than the red singlet line (Section 17). Bender concludes that 
a reaction of Zn(4 3 Pj) with H 2 is more probable than that of Zn (4 1 P ] ), 
because of better energy resonance ; the energy of the singlet state is 
5.77 eV or larger by 1.31 eV than the heat of dissociation of H 2 . 
However, it must also be taken into account that the lifetime of the 
singlet state is more than ten thousand times shorter than that of the 
triplet state (92). 

The quenching of the mercury and cadmium resonance radiation 
by saturated hydrocarbons is followed by polymerization and other 



120 MONATOMIC GASES AND VAPORS 

transformations of the organic molecules. The primary process is 
supposed to be of the same type as in the quenching by hydrogen (com- 
pare Section 74) : 

M* + C,^, -> MH + QH^ (30) 

The subsequent chemical reactions of the radicals need not be dealt 
with in this connection. The effective cross sections are relatively 
small (see Tables 14 and 15), with the exception of the heaviest 
compound (2 57, 589, 1063,1 558, 1559, 1561,1 563-1 565) . 

The effective quenching cross sections of the unsaturated hydro- 
carbons are much larger. In this case, the primary process is not 
connected with a photolysis of the compounds ; the electronic energy 
of the mercury atoms is transformed into excitation energy of the 
colliding molecule. For instance, for ethylene: 

Hg* + C 2 H 4 -> Hg + C 2 H 4 * (31) 

with subsequent reactions of the type : C 2 H 4 * -> C 2 H 2 + H 2 ; H + C 2 H 4 
-^C 2 H 5 ;etc. {699,903-905,1054,1560). However, ethylene absorbs only 
about 20 % of the total energy as electronic excitation energy ; the 
remnant must be transferred into vibrational energy of the molecule. 
(This would not be at variance with the Franck-Condon principle, since 
the molecules are transferred simultaneously to a different electronic 
state). Because of this great internal energy, it is not improbable 
that the primary reaction is followed by a dissociation of the excited 
molecule before the polymerization can occur. Such an event is much 
less probable if the process is sensitized by the presence of excited 
Cd (5 3 P X ) or Zn (4 3 P : ) atoms, because of the appreciably smaller 
excitation energies of cadmium and zinc {548a, 548b, 558, 589, 904). 

The quenching of the mercury resonance radiation by acetylene 
is ascribed to the analogous mechanism followed by a polymerizing 
chain reaction: 

Hg ("PJ + C 2 H 2 -> Hg (is.) + (C 2 H 2 )* 
(C 2 H 2 )* + C 2 H 2 -+ (C 2 H 2 ) 2 *; (C 2 H 2 ) 2 * + C 2 H 2 -> (C 2 H 2 ) 3 *; etc. 

This polymerizing process is inhibited by the presence of NO, perhaps 
due to the formation of C 2 H 2 NO {697,905,1012). 

Hydrogen-deuterium exchange reactions in mixtures of the 
vapors of ammonia, phosphene, or methane and heavy water are 
photosensitized by mercury vapor irradiated with the mercury 
resonance line {380,1013). 

Chemical reactions are known to occur in many processes by 



ENERGY TRANSFER IN QUENCHING COLLISIONS 121 

which the mercury resonance radiation is quenched but, in general, 
it is difficult to ascertain the mechanism of the primary energy 
transfer. When the resonance radiation is quenched by oxygen, the 
gas disappears gradually, while solid HgO is deposited on the walls; 
simultaneously the fluorescence regains its initial intensity if a 
sufficient supply of mercury is available (463,882,1148). If mercury 
vapor is excited in the presence of oxygen through a Mrozowski filter 
transmitting the hyperfine-structure components II and III of the 
line 253 7 A (Figure 19), only even isotopes are transferred into the 
state 6 3 P 1 and react subsequently with oxygen. In this way, a partial 
separation of the mercury isotopes can be achieved (1935) . 

If NO is the quenching gas, the gas pressure drops slowly to 
one-half of its original value (67,1629). According to Noyes, this is due 
to the formation of N 2 , while the oxygen reacts again with the mercury 
to form Hg 2 0. The sensitized photolysis of NH 3 and ND 3 by collisions 
with excited mercury atoms occurs, according to Melville, in two steps : 
by a first collision, the mercury atoms are transferred into the 
metastable state (see Section 37) ; by another collision of the metastable 
atom, an ammonia molecule is dissociated. This second process has 
a relatively small probability and is, therefore, very sensitive towards 
minute admixtures of hydrogen which "quenches" the metastable 
atoms before a second effective collision with an NH 3 - or ND 3 -molecule 
takes place (1011,1041,1150). 

While the quenching cross section of ND 3 for the mercury reso- 
nance radiation is appreciably smaller than that of NH 3 , corresponding 
to the greater energy deficiency As of — 0.072 eV against 0.016 eV 
(Figure 38), the quenching efficiencies of PH 3 and PD 3 are nearly the 
same, although, in this case too, the vibrational frequency of the 
ground state of PH 3 is in much better energy resonance with the 
transition 6 3 P t -»■ 6 3 P of the mercury atoms (As = 0.012 eV for PH S 
as compared with 0.07 eV for PD 3 ). Moreover, the quenching cross 
sections of the phosphines are much larger than that of ammonia 
(26 and 29-10 -16 against 4-10 -16 cm 2 ) and, finally, the mercury- 
sensitized decomposition of the phosphines is very little inhibited by 
the presence of hydrogen. It must be assumed, therefore, that, in this 
instance, a collision with an excited mercury atom produces the direct 
transition 6 3 P t -> 6 1 S and the decomposition of the colliding molecule 
with much greater probability than the transition 6 a P 1 -> 6 3 P , which 
would be due to the intake of vibrational energy by the phosphine 
molecules (1014). 

It is very improbable that the quenching of the sodium and 




A + M 



122 MONATOMIC GASES AND VAPORS 

thallium fluorescence is primarily due to chemical reactions of the 
excited atoms. If the foreign gas is monatomic, the formation of a 
molecule in a simple collision is impossible because of the conservation 
of momentum, even if the two partners are able to form a stable 
molecule. This applies, for instance, to the quenching of the sodium 
resonance radiation *by atomic iodine : the two atoms approach each 
other along a potential curve with a deep potential minimum, but, at 
the point of closest approach, they have sufficient potential energy to 
separate again along the same curve. This is true for the unexcited 
state as well as for the excited state of the sodium atom. However, 

Laidler has pointed out that the 
potential curves representing 
these two states may draw so 
near to each other at some point 
(Figure 49) that a transition from 
one to the other would no longer 
disagree with the Franck-Condon 
principle. 

If the same considerations 
are applied to the quenching of 

the sodium resonance radiation 
Fig. 49. Potential curves for quench- , , , •, , , 

. 5 .,, . . , r .. .. by molecular hydrogen and ni- 
mg without transfer of excitation J J ° 

energy (Laidler). trogen, or by hydrocarbons, the 

two-dimensional potential curves 
must be replaced by three-dimensional or polydimensional surfaces, 
since the relative positions of the individual atoms within the 
quenching molecules are aiso influencing the interaction with the 
excited atom. In this case, curves like that of Figure 49 would 
represent a cross section of such a potential surface {857). 

These statements are only a more elaborate formulation of a 
general idea which has been enunciated at a much earlier date by 
Franck and Eucken and has been repeated since by several authors 
in slightly different ways. The probability of the transfer of any kind 
of energy into vibrational energy of a molecule by a collision is large 
only if the potential curves of the molecule undergo a strong deformation 
by the interaction between the colliding particles, and this always 
occurs if one of the colliding particles is a radical or a chemically 
reacting atom or, more generally speaking, a particle with a strong 
external electric field. According to Eucken, every exchange of energy 
between two molecules must be treated as the beginning of a chemical 
reaction [414)- 



•r 



ENERGY TRANSFER IN QUENCHING COLLISIONS 123 

While the quenching of the mercury resonance radiation by 
saturated hydrocarbons is accompanied by a photosensitized reaction, 
this cannot be assumed for the quenching of the sodium resonance by 
the same compounds. Neither is the available energy sufficient, nor 
have such reactions actually been observed. Nevertheless, the quench- 
ing cross sections are of the same order of magnitude for the resonance 
radiation of mercury and sodium, and they are in both cases much 
smaller for the saturated hydrocarbons than for the nonsaturated 
compounds. The strong external fields of the latter have a much larger 
influence on the probability of the energy transfer than the possibility 
of an actual chemical process [6g8). 

The rare gases, like argon, are very weak quenchers, but they are 
not quite ineffective. They cannot take 
part in a chemical reaction nor take up 
electronic or vibrational energy. Attrac- 
tion curves with a potential minimum 
do not exist either ; but, at small nuclear 
distances r, the two repulsion curves I 
and II of Figure 50 can cross at b or at 5o -^ ^^ 

least can come so close together at y~y for quenching by a rare gas 
that a transition from one to the other [Jablonski {658)]. 

becomes possible. At this point of close I : metal atom in ground 
approach, the energy levels of the fluor- state. II: metal atom in 

, . t. j- i 1. j t- it. excited state. 

escent atom are so much distorted by the 

interaction with even a rare-gas atom that there is practically no dif- 
ference between the energy of the excited and the unexcited atom, a 
transition from one to the other consists only in a rearrangement of the 
electronic configuration. As these transitions occur at very small 
internuclear distances, the effective cross sections for quenching 
collisions of this type are very small and increase with increasing 
temperature. According to Oldenberg, the quenching efficiency of 
argon for the resonance radiation of mercury is very low at room 
temperature and becomes nearly four times larger when the tempera- 
ture is raised to 750° C. In this case the quenching is not caused by the 
transfer to the metastable state but by direct transfer to the ground 
state of the excited atoms so that the electronic excitation energy is 
completely converted into kinetic energy of the separating atoms 
{658,1167). 



124 



MONATOMIC GASES AND VAPORS 



H. Sensitized Fluorescence 

41. Nature of the Phenomenon and the Importance of Energy 
Resonance. The process which has been denned in the last section as 
sensitized fluorescence has the greatest probability of occuring if the 
foreign atoms colliding with the excited atoms have an electronic 
state with an energy very close to the excitation energy of the latter. 
The lines originating from this electronic state will have the greatest 
intensity in the spectrum of the sensitized fluorescence. In order to 
provide a sufficient number of collisions with the primarily excited 
atoms, the partial pressure of the second vapor must not be too low. 
Therefore, the lines leading to the ground state will be relatively 
weakened by reabsorption. If the energy resonance between the 
electronic states of the absorbing and the emitting atom is not very 







Tt(Cd) 



Fig. 51. Apparatus for production of sensitized fluorescence (Cario). 
S : light source. Q : resonance lamp. O t , O a , and O a : electric ovens. 



good, the kinetic energy of the colliding atoms may be so much in- 
creased that the reabsorption is considerably reduced. These theoreti- 
cal predictions which are due to Franck are in general agreement with 
the intensity distributions which were observed in the spectra of 
sensitized fluorescence. 

The phenomenon was discovered by Cario in a mixture of mercury 
vapor and thallium vapor irradiated with the mercury resonance line 
2537A (201,202b). The observation chamber and two side tubes were 
heated by three independent ovens so that the temperature of observa- 
tion and the vapor pressure of the two metals contained in the side 
tubes could be adjusted separately (Figure 51); the pressure of the 
mercury vapor was 0.25 mm and that of the thallium vapor, 2 mm. 
The fluorescence spectrum obtained under these conditions consisted, 
apart from the mercury resonance line, of a great number of thallium 



SENSITIZED FLUORESCENCE 



125 



arc lines. The thallium lines disappeared, together with the mercury 
resonance line, if the exciting water-cooled arc lamp was replaced by 
a hot mercury lamp {316). 

In the same way, sensitized fluorescence was later obtained in the 
vapors of the alkali metals, of silver, cadmium, zinc, lead, and indium, 
while experiments with antimony and arsenic gave negative results. 
In all these instances the primarily excited atoms were mercury atoms. 
Atomic fluorescence sensitized by light absorption in the vapor of 
another metal has not yet been observed (310,805,821,959(1,1845,1846). 

The earlier papers of the Goettingen school give the impression 
that, in spite of the preferential excitation of electronic states with 
small energy differences, the secondary emission of lines for which the 
available surplus energy exceeded 1 eV was directly stimulated by 
collisions with excited mercury atoms. Beutler's and Josephy's 
investigation of the mercury photosensitized fluorescence of sodium 
showed unambiguously the extraordinary importance of energy 
resonance for the efficiency of the energy transfer in sensitized 
fluorescence (100,103). (It must be emphasized, however, that even 
before the discovery of sensitized fluorescence J. Franck put forward, 
for the first time, the principle which bears his name). 

Table 20 
Energies of Various Na- and Hg-TERMS 



Na-term . . 
Energy in eV . 


iD 
4.26 


6S 
4.50 


5D 
4.58 


IS 
4.71 


6£> 1 8S 
4.75| 4.81 


ID 
4.84 


9S 
4.88 


8D. 
4.92 


105 
4.94 


Hg-term . . 
Energy in eV . 


6 3 -P &P X 
4.68 4.86 



Table 20 lists the energies of various terms of the sodium atom 
and, for comparison, the energy of two mercury terms. In general, 
the intensity of the lines of a series decreases rapidly with increasing 
order, so that the line 95 -> ZP is one of the weakest in the emission 
spectrum of sodium vapor under normal conditions. In the spectrum 
of sensitized fluorescence, however, this line is particularly strong, 
while the line 4Z) ->• 3P, which would be much stronger in a normal 
spectrum, is very weak. As shown in Table 19, the energy of the term 
95 is very nearly the same as the energy of the mercury level G i P 1 and, 
thus, the sodium atoms are transferred with greatest probability into 
the level 95 by a collision with an excited mercury atom. On the other 
hand, the lines corresponding to the transitions 95 ->- 3P (4423 and 
Pringsheim 5 



126 



MONATQMIC GASES AND VAPORS 



12523/21 
■ 2560 

1 2710 
12715 

1 2837 

1 2933 
13039 



4420A)* have the greatest intensity of all the lines originating from the 
state 9S. The effective radii, which were calculated from the intensity 
of the lines, the intensity of the primary radiation and the vapor 
densities, were several hundred times larger than the kinetic radii. 

By an addition of nitrogen to the mixture of the metal vapors, 
most of the excited mercury atoms can be transferred into the me- 
tastable state 6 3 P before they collide with a sodium 
atom. The state 6 3 P of mercury is in almost com- 
plete energy resonance with the Na-term 7S and, 
therefore, the line 7S ->• 3P (4750A) becomes pre- 
valent in the sensitized fluorescence spectrum of 
sodium under these changed conditions. 

Whichever of the two lines is emitted prim- 
arily, the emission of the D-Iines must always follow 
as a second step in the return from the state 3P to 
|3259/56 the ground state. As far as estimates of the relative 
intensities permit one to draw a conclusion, the 
emission of the D-lines was not excited in these 
experiments by any other more direct mechanism. 
(That the D-lines were found to be abnormally 
broadened under these conditions of excitation is 
no proof for a Doppler effect due to the transfer 
Fig. 52. Spectrum f a great amount of kinetic energy in a direct exci- 
tation of the state 3 P. Because of the relatively low 
mercury vapor pressure, the fluorescence was ex- 
cited in rather deep layers of the vapor, so that the 
D-lines were partially self-reversed on their way to 
the exit window). 

These results lead to a more comprehensive 
interpretation of the sensitized fluorescence which was observed in 
other metal vapors. The fluorescence of indium may serve as a typical 
example (310). The lines obtained by Donat are listed in Table 21, 
the spectrum is reproduced in Figure 52 and, schematically, in the 
Grotrian diagram of Figure 53. The resonance between the indium 
terms IP and 6D, with energies of 4.78 and 4.80, and the mercury 
level 6 S P 1 is sufficiently good. From these two states, stepwise trans- 
itions lead to all lower levels of the Grotrian diagram from which 
the lines of Figure 52 and 53 originate. As far as the lines 2602 and 
2521/23 are concerned, it must be considered that at an observation 

* The doublets were not resolved on the spectrograms and, therefore, the 
corresponding indices were omitted in the designation of the terms in Table 20. 



of Hg-sensitized 
fluorescence of 
indium (Donat). 

a : mercury spec- 
trum, b : fluores- 
cence spectrum. 



SENSITIZED FLUORESCENCE 



127 



temperature of 900° C an appre- 
ciable number of indium atoms 
are in the metastable state 5 2 P 3/2 , 
which lies 0.272 eV above the 
ground state. The transition 
7 2 D ■*- 5 2 P 3/2 in the indium atom 
is again in good resonance with 
the mercury line 253 7A. 

It is not possible to explain 
the line intensities observed in 
the sensitized thallium fluores- 
cence spectrum by similar con- 
siderations. The only thallium 
term with an energy close to 
the energy of the mercury state 
6 3 Pj is the term 8S, its energy 
being 4.77 eV. There are some 
lines in the spectrum originating 
from this level. Furthermore, the 
level 7S can be reached from 8S 
via IP and, thus, the occurrence 
of the strong lines 5350 and 
3776A (see Figure 9) can be 
understood. However, the line 
3529A originating from the level 
6D m (4.45 eV) is almost the 
strongest in the whole fluores- 
cence spectrum. A spontaneous 
transition 8S -» 6D is forbidden, 
and a primary excitation of the 
state 8P ]/2 , with an energy of 
5.11 eV, is also out of the qu- 
estion. Thus, it was assumed by 
Cario that the thallium atoms 
were directly transferred by col- 
lisions wtih excited mercury- 
atoms into the state 6Z) 3/2 with 
the relatively high surplus kinetic 

Fig. 53. Grotrian diagram of indium 



(Donat). 




30000 



Pringsheim 5* 



128 



MONATOMIC GASES AND VAPORS 



Table 21 
The Spectrum of Sensitized Fluorescence of Indium 



Wave 


Inten- 


Terms involved 


Energy eV 
of upper 


Wave 


Inten- 


Terms involved 


Energy eV 


length (A) 


sity 




term 


length (A) 


sity 




term 


4511 


v.st. 


65 llt- 5P sl» 


3.00 


2754 


Hg* 


IS j/j-5?^ 


4.46 


4102 


St. 


65 l/2- 5P l/2 


3.00 


2715 


w. 


&D 3l2-5 P 3h 


4.80 


3259 


v.st. 


5D 3 / 2 -5P 3 / 2 


4.04 


2710 


St. 


6D sh-5 p 3h 


4.80 


3256 


n.s. 


5 - D 5/2- 5 - P 3/2 


4.04 


2602 


v.w. 


8S J/2-5P3/2 


5.01 


3039 


St. 


SD sl2 -5P lh 


4.04 


2560 


w. 


eD sh~ 5P ih 


4.80 


2933 


St. 


IS xii-SPiit 


4.46 


2523 > ] 
2521J 


v.w. 


7D 3 , 2 -5P 3 / 2 


5.15 

(4.88)f 












7^ 5 /2-5P 3/2 


5.15 



v. st.: very strong: st.: strong; w. : weak; v.w. : very weak; n.s. : not separated. 

* Hidden by mercury line. 

t 5.15—0.27 = 4.88 (5P 3 / 2 -5P l/2 = 0.27 eV). 

energy of 0.41 eV divided equally between the two atoms. Despite 
the resulting Doppler effect, the small intensity of the other line 
originating from 6Z) 3/2 and leading to 6P 1/2 was ascribed to the re- 
absorption of this line in the thallium vapor (202b). 

However, it is very probable that many other processes have to 
be taken into account for a complete explanation of the phenomenon. 
Under the conditions of the experiment, a part of the excited mercury 
atoms may have been transferred into the metastable state by the 
interaction with other mercury atoms. Furthermore, excited Hg 2 - 
molecules can be formed by collisions of normal Hg-atoms with 
mercury atoms in the states 6 3 P or 6 3 .P\. The very complicated 
potential-curve system of these molecules is shown in Figure 81. 
Finally, excited mercury atoms may combine with thallium atoms to 
form excited HgTl-moleculesand these may dissociate later into normal 
mercury and excited thallium atoms. 

Insofar as the second of these assumptions is concerned, Mrozowski 
has actually shown that sensitized thallium fluorescence can be pro- 
duced by primary excitation of Hg 2 -molecules, although it is true that 
in his experiments the mercury vapor pressure was appreciably higher. 
Under these conditions, the sensitized thallium fluorescence was ex- 
cited by primary lines which are not absorbed by monalomic mercury 
vapor {ioygb). (This process will be dealt with in more detail in 
Section 79). 

As mentioned in Section 39, the resonance radiation of mercury 
is almost completely quenched in mercury vapor saturated at 250° C ; 



SENSITIZED FLUORESCENCE 129 

simultaneously, the lines of the sensitized thallium fluorescence not 
only become stronger than at the mercury vapor pressure most 
favorable for the emission by the mercury atoms themselves, but the 
intensity of the thallium line 3776A does not decrease if the mercury 
vapor pressure is raised to more than an atmosphere (350°). The 
thallium vapor pressure need not exceed a few hundredths of a mm 
so that an excited mercury atom or molecule will, on the average, 
collide with a thallium atom only after 10,000 collisions with other 
mercury atoms. According to Mrozowski's later observations, it can 
hardly be doubted that in these experiments also, not only metastable 
Hg-atoms but Hg 2 -molecules contributed, at least partially, toward the 
conservation of the excitation energy over so long a period (1182). 

The third hypothesis mentioned above is supported by two facts. 
The formation of HgTl-molecules under favorable conditions has been 
proved by the appearance of emission bands characteristic of these 
molecules. On the other hand, the emission of the 'mercury resonance 
line following the dissociation of excited Hg 2 -molecules has been 
observed in many experiments. 

A few lines occur in the sensitized fluorescence of thallium which 
require excitation energies of up to 5.5 eV, since they originate from 
the levels 8D and 9S. Their appearance can be explained by the fact 
that at 800° C a small fraction of the thallium atoms is in the meta- 
stable state 6P 3/2 , as proved by noticeable absorption of the green line 
in the vapor. From 6P 3/2 , the thallium atoms can be raised with 
fairly good energy resonance into one of the higher P-states by col- 
lisions with excited mercury atoms (for instance 1 1 P-6P 3/2 = 4.81 e V) . 
(This mechanism cannot suffice to explain the appearance of the strong 
line 3529A in the fluorescence spectrum). 

At a temperature of 800° C in the observation chamber, the lines 
of the Cd-triplet 5086-4800-4678A were obtained in the mercury 
sensitized fluorescence of cadmium vapor, though with very small 
intensity. These lines require an excitation energy of 6.3 eV. If the 
vapor pressure is kept constant while the temperature in the obser- 
vation chamber is lowered to 400° C, the lines disappear. Thereby it is 
proved that the surplus energy actually is furnished by thermal 
agitation, and since the cadmium atoms have no metastable state of 
higher energy above the ground state like the thallium atoms, this 
energy must be provided either by the transferring collision itself or 
by a second collision during the life of the excited state. The average 
kinetic energy of the atoms is only 0.11 eV and, thus, collisions with 
a surplus energy of 1.4 eV would be exceedingly rare. The improba- 



130 MONATOMIC GASES AND VAPORS 

bility of a transfer of so large an amount of kinetic energy into elec- 
tronic excitation energy has already been sufficiently discussed. One 
may, therefore, have to assume, in this instance also, a more compli- 
cated mechanism. 

The same consideration applies even more convincingly to the 
appearance of lines with an excitation energy of 7.7 e V in the mercury 
sensitized fluorescence of zinc vapor at a temperature of only 720° C 
(for instance, the line 3302A, 4 3 D 2 -4 3 Pj). Since this energy surplus 
can under no circumstances be supplied from the thermal energy, 
Winans assumed that mercury atoms are raised by stepwise excitation 
into a higher level — for instance, by secondary absorption of the line 
4358A into the state 7 3 S X with an energy of 7.69 eV. This process was 
possible in Winans' experiments because the full radiation of a mer- 
cury arc was used for excitation. The same is true for all observations 
mentioned in this section. By inserting a filter which transmitted only 
the mercury line 2'537A into the path of the exciting radiation, the 
zinc lines requiring a high energy were suppressed in the fluorescence 
spectrum. However, it is certain that, at least in part, the observed 
emission lines were not caused by any kind of absorption in mercury 
atoms; for, in contradistinction to Cario's original experiment with 
thallium vapor, some of the zinc lines were excited also by light of a 
hot mercury lamp which could not stimulate resonance radiation in 
pure mercury vapor, while another part of the zinc lines disappeared 
under these conditions. Furthermore, it was possible to excite the 
zinc fluorescence (the lines of the triplet 5 3 S 1 -4 a P 0ih2 ) by irradiating 
the mixture of mercury and zinc vapor with light of wavelengths 
below 1900A produced by an aluminum spark. Although Winans 
ascribed the absorption of this radiation to mercury atoms, it was 
probably caused by molecules of some sort, either Hg 2 or Zn 2 or HgZn. 
Actually, a band which belonged neither to pure Hg- nor to pure Zn- 
vapor was observed in the absorption and emission spectra of the 
mixed vapors. Winans' experimental conditions were particularly 
favorable for the formation of molecules of this type because the zinc 
vapor pressure was very high (16 mm) (1845-1847). 

The investigation of the sensitized fluorescence of the other metals 
enumerated in the third paragraph of this section corroborated the 
foregoing conclusions, more or less, without providing further infor- 
mation of importance. 

Winans devised a simplified method for the excitation of sensitized 
fluorescence, especially of metals such as iron and chromium which 
have very low vapor pressures at moderate temperatures. The metal is 



INFLUENCE OF FOREIGN GASES AND MAGNETIC FIELDS 131 

crushed to a fine powder and introduced into a quartz tube containing 
some mercury. The tube is evacuated and the part containing the 
powder is heated with a blowtorch to the highest temperature which 
the tube stands without collapsing. The mercury pressure is adjusted to 
values between 1 and 150 mm by keeping the coldest part of the tube 
at an adequate temperature. When the radiation from a water-cooled 
mercury arc was focused on the hottest part of the tube, the two 
resonance triplets of chromium (at 3600 and 4300A) and some thirty 
iron lines could be obtained in the sensitized fluorescence spectrum of 
these metals (1850,1854}. 

Winans used the same method for the excitation of the sensitized 
fluorescence of lead and tin, and here it could be shown that, although 
with lesser efficiency than the energy resonance, a "partial selection 
rule," A J = 0, is of importance for the transfer of energy; the proba- 
bility of transfer is greater if the sumof the electronicangularmomenta 
of the two colliding atoms, Hg* and M[/= J(Hg) + /(M)], remains 
constant and is smaller if / changes. If the excitation of lead atoms is 
mainly due to collisions with Hg ( 3 P )-atoms (e.g., if nitrogen is pre- 
sent in the tube) and thus the value of /(Hg) is zero before and after 
the collision, the lead line 3683A originating from the level 3 PJj is much 
stronger than the line 3639A originating from 3 PJ (Figure 10), while 
in the arc spectrum of lead the two lines have practically the same 
intensity. The energy difference between the two levels is so small that 
they are equivalent insofar as energy resonance is concerned. Similar 
considerations can be applied to a pair of lines in the spectrum of tin, 
in which altogether thirteen lines have been obtained by the excitation 
of sensitized fluorescence (i84g, 1852, 1855). 

42. Influence of Foreign Gases and of Magnetic Fields. If, by 
addition of nitrogen, the excited mefcury atoms are transferred to the 
metastable state 6 3 P , the probability of collisions of the second kind 
is greatly increased. Donat has actually observed that in the sensitized 
fluorescence of thallium, the thallium lines were considerably enhanced 
if nitrogen was added to the mixture of the metal vapors. According to 
Donat, the various thallium lines behave very differently under these 
conditions: some of them (2920, 2580, 3230, 3530A) reach an intensity 
maximum at 30 mm of N 2 and fade out rather rapidly at higher 
nitrogen pressures; others (3551, 3776A) remain constant between 
30 mm and one atmosphere, while the intensity of the line 2788A, 
with a slower initial rise, continues to increase up to atmospheric 
pressure. However, these results were not confirmed by Loria, who 
states that all lines decline again with increasing nitrogen pressure 
Pringsheim 5** 



132 MONATOMIC GASES AND VAPORS 

after having reached a maximum intensity. Since no other observa- 
tions are available, a discussion of these discrepancies is not possible. A 
decrease of the fluorescence intensity at high nitrogen pressures is 
plausible in itself because of the quenching action of the gas on the 
fluorescence of thallium (Table 16). Both authors agree that argon 
produces similar effects, although considerably higher pressures are 
necessary. However, it is very likely that the action of argon was due 
to traces of nitrogen, since it has been shown repeatedly that a transfer 
of excited mercury atoms into the metastable state practically never 
occurs by collisions with argon (310,960,1182). 

The enhancement of the thallium lines by the addition of nitrogen 
is not only inhibited by the presence of the smallest traces of oxygen 
or hydrogen, but the light emission is completely quenched as soon as 
the probability of a collision of the metastable atoms with the mole- 
cules of these strongly quenching gases becomes larger than the pro- 
bability of a collision with a thallium atom. The direct quenching 
action of oxygen (not of hydrogen) on the thallium fluorescence must 
also be taken into account (310). 

The great influence of the presence of nitrogen and of the resulting 
production of metastable mercury atoms for the sensitized fluorescence 
of sodium vapor has already been discussed (Section 41). If mercury 
vapor is irradiated at room temperature in the presence of 3.7 mm 
of nitrogen with the resonance line alone and, thus, under conditions 
which exclude stepwise excitation, the lines 3662, 3665, and 3650A 
are observed in the fluorescence spectrum. Beutler and Rabino witch 
consider this phenomenon to be due to a kind of sensitized fluorescence 
between mercury and mercury atoms and designate it as "energy 
enhancement in an elementary process" {105). The energy levels from 
which the lines mentioned above originate are 6 3 D 1)2;3) 8 3 S 1: and pos- 
sibly 8^0 (compare Fig. 1 5) ; they have excitation energies of 8.81 , 9. 1 3, 
and 9.20 eV, respectively. The last value corresponds almost exactly 
to the sum of the energies contained in two 6 3 P -atoms and can, there- 
fore, be transferred with excellent energy resonance to one atom by a 
collision of two metastable atoms. The resonance would still be suffi- 
ciently good for the excitation of the state 8 3 S (9.13 eV), the small 
surplus energy being converted into thermal agitation. The 6 s D- 
states are probably produced by subsequent collisions of 8S-atoms 
with nitrogen molecules which are able to take up the energy difference 
of 0.27 eV as vibrational energy. 

Beutler and Josephi suppose that even the photoelectric ioni- 
zation of mercury vapor, which was discovered by Steubing and which 



INFLUENCE OF FOREIGN GASES AND MAGNETIC FIELDS 133 

is produced by irradiating the vapor with the resonance line, may be 
due to another repetition of the same process. After being raised to 
the state 8 1 S , an atom is assumed to take up the energy of a third 
metastable atom in a collision of the second kind. Although a quali- 
tative calculation proved that such processes might occur with suffi- 
cient abundance, it seems more likely, as has been discussed in detail 
by Houtermans, that, at least at higher vapor pressures, the formation 
of metastable excited Hg 2 -molecules and subsequently of Hg 2 -ions 
plays an important part in the process (103,105,630,1572). 

Mitchell investigated the sensitized fluorescence of cadmium at 
a mercury vapor pressure of 10~ 3 mm and a cadmium vapor pressure 
of 0.5 mm, in the presence of 2 mm of helium ; the observation chamber 
was placed in a magnetic field of 300 gauss with its lines of force 
parallel to the exciting radiation (case II). Under these conditons, the 
mercury resonance line was still appreciably polarized, while the 
cadmium line 3261 A showed no sign of polarization. Mitchell draws the 
conclusion from his observation that the primarily existing orientation 
of the electric vector is completely destroyed in an energy transfer by 
a collision of the second kind. Although the conclusion may be correct 
in itself, this is not proved unambiguously by the experiment. The 
partial polarization of the mercury line might persist in spite of the 
relatively high pressures of helium and cadmium vapor, while the 
cadmium line is completely depolarized by the resonance interaction 
between excited and unexcited cadmium atoms (1038). 



CHAPTER II 

DIATOMIC GASES AND VAPORS 

A. Theory of Band Spectra and Interpretation of 
Resonance Spectra 

43. Energy Levels. The internal energy of a diatomic molecule is 
not completely determined by the configuration of its electrons; it 
depends also on the vibrations of the nuclei along the line connecting 
them and on the rotation of the molecule around its principal axis of 
inertia, which is perpendicular to this line. In a first approximation, the 
total energy is obtained by the addition of three terms corresponding 
to the electronic, the vibrational, and the rotational energy : 

W = T + G + F (32) 

To the same approximation, the wave function describing the energy 
state of a molecule can be split into three factors : 

<F = W e - Wv-Vr (32a) 

¥^, W v , and W r depend only on the configuration of the electrons, on 

the nuclear vibration, and on the rotation of the molecule, respectively. 

The vibrational energy* of a strictly harmonic oscillator is : 

G(v) = (v + V,)«> (33) 

where to is the characteristic frequency of the oscillator and v = 
0, 1, 2 ... is the "vibrational quantum number." For an anharmonic 
oscillator, a term quadratic in v (and for a more accurate description 
also a cubic term) must be introduced into the ^equation, so that : 

G(V) =(V+ 7,K — (» + 1 l») t *eO> t + (V + 1 / 1 ) a y e O) e + ■■■ (34) 

o> e now being the frequency of the oscillator for vanishingly small 

* In this chapter all energies are given in cm -1 , for the sake of simplicity; 
in order to obtain the actual energies, all equations must be multiplied by hjc 
(compare Section 1). Following the common practice the symbol v is used in- 
stead of v for the wave number (compare Section 6). 

134 



ENERGY LEVELS 135 

amplitudes (v = 0). Even in the "vibrationless state" the energy of 
the oscillator is not zero but assumes the value : 

G (°) = V*o>« — i/tXtto, + . . . (35) 

The fraction of the molecular energy due to the rotation alone is : 

F(J) =/(/ + 1)-A/8*»I =/(/ + 1)-B (36) 

/ is the moment of inertia of the molecule with respect to its principal 
axis, and/ is the rotational quantum number. f 

The moment of inertia / and, therefore, also B, depend on the 
distance between the nuclei; they vary with the amplitude of the 
vibration and are functions of v : 

B v = B e — a(v + i/ 2 ) + . . . (37) 

a is the "coefficient of interaction" (between oscillation and rotation) 
The values x e , y e , B e , and a are characteristic of a given electronic 
state of a molecule and vary with the transition from one state to 
another. 

The frequency of a line corresponding to the transition from a 
state T', v', J' to a lower state J", v", J" is thus determined by the 
equation : 

V = (T'—T») + (G' — G") + (F' — F") (38) 

= v e + (»' + V.K - (v' + l /2) 2 *X - (V + VaK 

+ (»* + Vi)**X + /'(/' + 1) \B. - a'(V + i/,)] 

— /'(/"+ 1) [B; — a'(o' + V,)] 

In practical spectroscopy it is more convenient to use integer coef- 
ficients instead of the (v + 1 j^j values of the vibrational quantum 
numbers : 

v — v e + v'co — v' 2 x m — v"co" + v" 2 x" co" 

' 

+ JV + 1) (B„' - V') - J"(J" + 1) (B' 9 - ay) (38a) 

The constants occurring in Equation (38a) are derived easily from the 
constants of Equation (38) — for instance (neglecting y) : 

<°o = ">£(! — #e)> Vo = ^w„ etc. (38b) 

Taking into account the selection rules which are explained in the 

* If the rotor is not rigid, so that the distance between the nuclei is 
increased by the centrifugal acceleration, a term J l (J + l) 2 -£> must be added. 
However, this term can be neglected for the following considerations. 

t Compare Section 45 on the general Tneaning of the quantum number /• 



136 DIATOMIC GASES AND VAPORS 

following sections, Equations (38) and (38a), respectively, describe the 
complete band spectrum of a diatomic molecule. The first term on the 
right-hand side of these equations corresponds, by itself, to a line in 
the visible or ultraviolet region and contributes by far the largest part 
Of the total energy ( v e ~ 20,000 cm" 1 ). If a single electronic transition 
is considered, v e is kept constant and its value determines the approxi- 
mate position of a "band system" in the spectrum. In the second 
term, which corresponds to a variation of the vibrational energy, the 
frequencies w' and w" are, in general, of the same order of magnitude 
(in most cases between 100 and 1,000 cm" 1 ). (In the spectra of H 2 , N 2 , 
2 and some other gases and vapors, the values of a> are considerably 
larger) . 

Infrared vibrational bands correspond to transitions from one 
w-level to another, if they occur without a simultaneous electronic 
transition . 

If the rotational energy is disregarded [F = in Eq. (32)], the 
energy levels of three electronic states are represented by the diagram 
of Figure 54. The intervals AG between the individual sublevels of a 
given electronic state are constant, to a first approximation, but they 
decrease slowly from the bottom towards the top because the binding 
force between the nuclei is not strictly linear. Therefore, AG = <*> must 
be replaced by : 

AG(v + V.) = G{v + 1) — G(v) (39) 

= m e — • 2(v + \)x e (i> e 
= <u — 2(v + 1 / 2 )X (O 

For high values of v which, however, cannot be extrapolated from 
Equation (38) without taking the cubic term and, possibly, even 
higher-order terms into account, AG converges towards zero; the 
vibrational levels converge towards an upper limit where they merge 
into a continuum corresponding to a complete separation of the two 
nuclei. The atoms or ions into which the molecule splits can acquire 
kinetic energies which are no longer quantized. 

If all excited molecules of a vapor are in one definite vibrational 
level v' of an electronic state T', they can return from there to all 
existing levels v" of the ground state and thus produce an emission 
spectrum in which the lines corresponding to v" = 0, 1 , 2 . . . form 
a regular "progression." The intervals between neighboring lines in the 
progression decrease according to Equation (39). Without a simul- 
taneous electron jump, the vibrational number v of a harmonic 
oscillator can vary only by ± 1 ; values of Av larger than one can 



ENERGY LEVELS 



137 



occur only to the extent to which the binding force of the oscillator is 
anharmonic ; the probability of such transitions decreases rapidly with 
increasing Av, if the anharmonicity of the oscillator is small {x<^ 1), 
a condition which holds for practically all diatomic molecules. Lenz 



4 

I 















































































J«4 



6 -I 

5 i J 

4 i _L 

3 J p.!- 

2 -Li L__ 

i — i Lj — _ 

n :: :; 



{<4<?,(4£) 






Fig. 54. Energy-level diagram for two band systems of a 
diatomic molecule. 



has shown, however, that if an electronic transition (or, in the corre- 
sponding classical model, an electronic vibration) is superimposed on 
the nuclear vibrations, the two processes will influence each other even 
according to classical electrodynamics. Under quite plausible assump- 
tions regarding this interaction, overtones of high order or transitions 
with large Av may be expected to occur in the nuclear vibrations, 
although the binding force between the nuclei may be strictly linear. 
Under these conditions, the intensities of neighboring lines of the 



138 



DIATOMIC GASES AND VAPORS 



progression can vary in a very irregular fashion, as has been actually 
observed. The quantum-mechanical interpretation of this phenomenon 
is discussed in Sections 47 and 48 (8g8,8gg). 

44. Rotational Doublets and the Complete Resonance Spectrum. 

The last term on the right-hand side of Equation (38) is due to 
molecular rotation. Thereby, every line corresponding to a transition 
v' -»• v" splits into a multitude of lines forming a "band." The scheme 
of Figure 54 does not take the molecular rotation into account ; the 
energy levels are drawn for/ = 0. If all levels caused by the variation 
of / were included in the diagram, a series of levels would be inserted 
above every horizontal line of the figure. The distances between these 
levels would steadily increase according to the following relation, 
which is derived from Equation (36) : 



AFV + Vi) = F(T + 1) - FV) = 2(/ + 1)B 



(40) 



The higher members of these series would stretch beyond the following 
vibrational levels, so that the ground would be covered almost con- 




\ 'I UK-/? 

I lOl 9| 8l7ll 



4 3 2 1 12 3456 

« P *R 

DIRECTION OF INCREASING FREQUENCIES 



Fig. 55. Fortrat diagram for a band system with 
P-, Q-, and i?-branches. 



tinuously and the diagram would be completely blurred. It is better, 
therefore, to represent the subdivision of the energy levels caused by 
the molecular rotation by a different scheme, reproduced in Figure 55 



ROTATIONAL DOUBLETS AND COMPLETE RESONANCE SPECTRUM 139 

— so-called Fortrat parabolas. The scheme is not quite as simple and 
obvious as that of Figure 54, but it has the advantage of showing 
only the allowed transitions, which occur by varying / and it makes 
possible a direct visualization of the relative position of the corre- 
sponding lines in the band. 

The rotational quantum number follows the selection rule AJ = 
or ± 1 strictly, so that always J" = J' or J" = J' ± 1. Thus, the 
last term in Equation (38) can assume the three following forms: 

a: J" = J' — 1 : P(J") = J'*{B-B" v ) + J"(B V + b" v ) (41) 

= /i (B-BJ +J> { B-B" v )-B" v + (2/' + 1)B" V 
b: /' = /': QUI = J"[B—B' V ) +J'(B-B V ) 

c :/*=/' + URW) = J'HB-Bl) +J' { B-3Bl)-2B" v 

= J' 2 (B-Bl) +J> { B-B" V )-B~-(2J'+1)B" V 

Each band is divided into three branches (P, Q, R), represented by 
parabolas in the diagram of Figure 55.* In all bands in which fluo- 
rescence spectra have been observed so far, AJ is either equal to or 
to ± 1; therefore, either only one rotational line corresponds to a 
transition from a given excited state T', v', J' to a vibrational level of 
the ground state T", v" , J" with J" = J', or two rotational lines of the 
band appear, corresponding to /" = J' + 1 and J" = J' — 1 and 
forming a doublet. The separation between the components of the 
doublet is: 

dv = (4/' + 2)B' V = (4/' + 2) {B-a"v") (42) 

Within a series corresponding to transitions from the same excited 
state v', J' to all vibrational levels v" — 0, 1, 2 . . . of the ground 
state, the doublet separation is approximately constant and decreases 
only slowly with increasing v" because of a <^ 1 . For various initial 
rotational states J', however, the values of Sv vary considerably; to 
a first approximation, they are proportional with AJ' . 

If the initial state T', v' , J' remains constant while the final state 
of an emission process assumes all possible values v", the terms of 
Equation (38a), which remain unaltered under these conditions, can 
be summed up into : 

* According to whether B Q is larger or smaller than Bq, the parabolas 
follow the direction of increasing or decreasing j> with increasing values of /'; in 

Figure 55 the latter assumption (Bo < Sol) has been made, since this is the case 
for almost all the examples occurring in this book. 



140 DIATOMIC GASES AND VAPORS 

v* = v e + v'<o'—v'\m' o + /'(/' + l)B t (l + dv') (43a) 

v* is the frequency of the line which would correspond to a transition 
to the final state v" — 0, disregarding the rotational energy. Intro- 
ducing this frequency v*, a complete doublet progression is repre- 
sented by the equation : 

v = v* + v"<o" o + v^xy—W ± 1) (/' + 1 ± l)B o "(l-aV) (43b) 

If strictly monochromatic light is absorbed in a vapor consisting 
of diatomic molecules, its frequency must coincide with that of an 
individual line of the band spectrum described by Equation (38a). 
Only molecules which are in a definite initial state t", v", /"* can take 
part in the absorption process and these are all transferred into the 
same excited state T', v', J'. In the absence of perturbations by 
collisions, etc., this state becomes the initial level from which the 
emission of a singlet or doublet series originates according to the 
mechanism described above. These "resonance series" have a very 
simple structure as compared to a complete band system; thus, the 
analysis of the band system is materially facilitated if some resonance 
series can be isolated. If, for instance, the values of v" and /* can be 
determined in a special case, the doublet interval in the series gives 
directly the molecular constants B" and a , and, simultaneously, the 
moment of inertia 1^. 

In practically all resonance spectra of diatomic molecules which 
have been observed so far, the molecule returns by the emission pro- 
cess to the electronic ground state. Under these conditions, the exciting 
line is also a line of the fluorescence spectrum. However, it is the first 
member of the progression only if v" = 0, or if the absorbing molecule 
contains no vibrational energy; otherwise, the emission spectrum 
exhibits a number of "anti-Stokes" lines with wavelengths smaller 
than that of the exciting line. 

Line progressions of this type were discovered by R. W. Wood in 
the fluorescence spectra of sodium and iodine vapor and were called 
by him "resonance spectra." It seemed obvious that a preferential 
position in the series should be ascribed to the exciting line, which was 
designated as the i?-line (resonance line) and characterized by the 
order number 0. The other lines were numbered with reference to the 
.R-line so that the order of the anti-Stokes lines became negative : 

* Terms and quantum numbers representing the state of a molecule 
previous to the exciting absorption process are designated by a bar above the 
symbol in the following chapters. 



ROTATIONAL DOUBLETS AND COMPLETE RESONANCE SPECTRUM 141 

v — vk — pa -f- p*b 
{p = 0, ± X, ± 2, ± 3 . . . is the "order number") (44) 

If a series is described cofrectly by Equation (43), it can also be re- 
presented by Equation (44) ; the constants occurring in (44) can be 
derived from those in (43) by simple transformations. However, the 
notation of Equation (43) has the advantage that ojq is a genuine 
molecular constant and retains the same value for every progression 
of the band system, while the constant a in Equation (44) is different 
for every series. The interval between the i?-line and the line which 
follows in the direction of greater wavelengths (p — + 1) is determi- 
ned by the relation: 

AG"{v R + V*)' = <o' e — 2[v' R + X)x" e w" t (45) 

and since b — x" e <o" e , it follows that a = ca" e — (2v~ R + \)x" e ai" e . 

The relative position of the doublet components in a resonance 
spectrum is essentially determined by the fact that the exciting ab- 
sorption line belongs either to the P- or to the i?-branch of the band — 
i.e., that in the absorption process the rotational quantum number/" 
increases to j" + 1 or decreases to /" — 1. In the first case, the com- 
panion line of the resonance line corresponds to the transition Q" + 1) 
-*■(/* 4- 2) and appears on the long-wavelength side of the i?-line; 
in the other case, the companion line corresponds to the transition 
{j" — 1) -> (/" — 2) and appears on the side of smaller wavelengths. 
In other words ; if the exciting line belongs to a P-branch, the com- 
panion line lies on the JR-branch, and vice versa. This is repeated in all 
other doublets of the. resonance spectrum. 

If the exciting line is broad enough to cover several absorption 
lines with various /"s and belonging partly to P- and partly to R- 
branches, the fluorescence spectrum consists no longer of doublets, 
but of complicated groups of lines which surround the central line more 
or less asymmetrically. 

If a further electronic level B exists above the excited state A, 
and if spontaneous transitions from B to the ground state N are 
allowed, resonance spectra of the same kind as in the band system 
A-N can be stimulated in the system B~N. They will be shifted 
towards shorter wavelengths, according to the greater energy dif- 
ference B-N; but the spacing AG(v + 1 / 2 ) within the series is the same 
as in the system A-N, since it is determined by the constants charac- 
terizing the ground state, which is common for both systems. The 



142 DIATOMIC GASES AND VAPORS 

occurrence of fluorescence spectra of diatomic molecules caused by 
stepwise transitions from a higher electronic state (B -> A, A ->N) 
has not been proved with any certainly. 

45. Electronic Terms. The electronic terms of diatomic mole- 
cules are discussed here only insofar as necessary to understand the 
designations which are used for the description of actually observed 
fluorescence spectra. For more details, reference should be made to 
books dealing exclusively with this subject.* 

The electronic quantum numbers I and s, or L and S, respectively, 
retain the same meaning as in Section 12. From these the new quantum 
numbers A and 2 are derived by projecting L and 5 upon the prin- 
cipal axis of the molecule. The molecular states 2,11 A . . , are deter- 
mined! by the quantum number A = 0, 1,2 . . . In the so-called 
"coupling case a," which alone may be discussed here as one of the 
most important instances, A and 2 combine vectorially to a new 
quantum number Q so that : 

\A — £\ <A< \A + £\ 

Q plays the same part as the inner quantum number in atomic spec- 
tra. In Sect. 43, / was characterized as the rotational quantum number 
of the molecule. Actually, J measures the total angular momentum of 
the molecule, which is determined by the superposition of the rota- 
tion of the nuclei around the principal axis of inertia, the orbital 
angular momentum of the electrons, and the spin of the electrons 
(and, in certain cases, of the nuclei). Thus, / is equivalent to the 
angular momentum M produced by the rotation of the molecule 
around the axis of inertia only for 1 2' -states. In all other cases, J 
differs from zero even in the absence of molecular rotation (M = 0), 
and the lowest value which can be assigned to / is 1 / 2 or 1 or 3 / 2 , 
etc., according to the nature of the electronic state and the values of 
L and S. 

In the "coupling case b," A and M combine by vectorial addition 
to a new quantum number K, and J is obtained by vectorial addition 
of K and the electronic spin 5. These altered definitions of / do not 
alter the representation of the resonance spectra given in the preceding 
sections. 

* Jevons, Report on Band Spectra of Diatomic Molecules, London, 1932; 
W. Weizel, Bandenspehtren : (1), Erganzungsband des Handbuchs der Experimen- 
talphysik, Akademische Verlagsgesellschaft, Leipzig, 1934; G. Herzberg, Molecu- 
lar Spectra and Molecular Structure, Prentice Hall, New York, 1939. 

f Like S in the description of atomic spectra, Z is used here in two different 
meanings : as a quantum number and as a term symbol. 



ELECTRONIC TERMS OF DIATOMIC MOLECULES 



143 



The most important selection rules for transitions between elec- 
tronic states are : 

AA = or ±1; AS = 0; Jfl = 0or±l; AS = or ± 1 

The multiplicity r of an electronic state, which is determined by the 
relation r = 2S + 1, can, therefore, change in an electronic transition 
by or ± 2. Allowed transitions are, for instance: 

l z -* l s\ m^ -> m x ; *n a -* 3 ir ; ^ -> *s 1 ■, m x -> i s n , etc. 

and forbidden transitions: 

3 77 -+ 3 I7 3 ; 3 n -* 3 A i ; 14 -> *.£i, etc. 

Other selection rules, particularly for element molecules con- 
sisting of two atoms of the same kind, follow from the fact that certain 
symmetry properties of the molecules must be preserved. 

1. A state may be positive (+) or negative ( — ). (See footnote at 
the end of 5). 

2. A state of an element molecule (which may consist of two 
isotopes o'f different mass) is called even (g), if the total angular 
momentum of its electrons is even : L = 0, 2, 4 . . . ; it is called odd 
(w) for odd values of L (L = 1, 3, 5 . . .). If necessary, g and u are 
added as subscripts to the term symbols : 

i-Sg, 2 i7j„, etc. 

3. A state of a homonuclear molecule is symmetrical (s) or 
antisymmetrical (a). A symmetrical state is always either positive 
and even (+ and g) or negative and odd ( — and u); an antisym- 
metrical state is always negative and even ( — and g) or positive and 
odd ( + and u). These relations and the corresponding selection rules 
are collected in Table 22. 



Table 22 
Allowed and Forbidden Transitions 



s 


a 


Allowed 


Forbidden 


+ andg 


+ and m 


S *± S 


s *± a 


— and u 


— and g 


a +£ a 


+ ->■ + 






+ ±5 — 


s- 






g itu 


g-> g 



144 DIATOMIC GASES AND VAPORS 

4. If a 27-state (A = 0) is produced by the action of two or more 
electrons with individual A > (e.g., A x = + 1, A 2 = — 1 otX 1 = + 1, 
A 3 = + 1, A 3 = — 2, etc.), the two sublevels Z + and Z~ have opposite 
symmetry properties and are, in general, separated by a rather large 
energy difference. In all other electronic states of a homonuclear mole- 
cule (17, A, etc.), each rotational level is split into two sublevels cand 
d which coincide energetically for / = and become gradually wider 
apart as J increases, c and d have opposite symmetry. This "/1-type 
doubling" is caused by the magnetic field which is produced by the 
rotation of the molecule ; according to whether A is parallel or anti- 
parallel to the lines of force of this field, the energy of the term is 
slightly different. 

5. The rotational levels of a given electronic state are alternately 
+ and — and, in a homonuclear molecule, alternately s and a; if, 
for instance, in a 77-state c is positive and, therefore, d negative for 
a given value of/, the reverse is true for/ + 1, where c is negative and 
d is positive.* 

It follows from 1, 2, and 3 that two states which combine with a 
third state cannot combine with each other. However, this rule applies 
strictly only to homonuclear molecules. In molecules of this type, 
consecutive rotational levels which are alternately symmetrical and 
antisymmetrical have unequal statistical weights. Hence, the con- 
secutive lines of a band have alternating intensities. 

The diatomic molecules of even elements (without nuclear spin ; 
sompare Section 12) have only symmetrical terms; every second term 
with an odd value of K ox J, respectively, is missing. For odd elements, 
the nuclear spin i is always different from zero, and the ( — , g) or the 
( +, w) terms ("ortho terms") have a larger statistical weight than the 
(+,g) and the ( — , u) terms ("para terms"). 

For Z -*■ Z transitions, the Q-branches are missing in all bands, 
A J = being forbidden for A = 0; the resonance series consist of 
doublets exclusively (example: the green resonance spectra of I 2 ). 
In bands corresponding to transitions Z **TI, (^-branches are not only 

* The meaning of these symmetry relations can be explained only in terms 
of quantum mechanics. An electrone state is + if the wave function W corre- 
sponding to the motion of the electrons with regard to the nuclei does not change 
its sign on reflection in a plane through the axis of the molecule. A state is g 
(from the German gerade) if the electronic factor of W VP e in Equation (32a)] 
does not change its sign on reflection in the midpoint of the line joining the two 
nuclei. A state is symmetrical if on interchanging the two nuclei *P e does not 
change its sign. — , u, and a are determined by a change of sign in W e under the 
conditions mentioned above. 



SHAPE OF POTENTIAL CURVES OF ELECTRONIC STATES 



145 



present, but their intensity is even greater than that of the P- and 
i?-branches. It follows from 4 and 5 that if in this case 27 has the same 
symmetry as 11(c) for a given value of 7 = J„, and, therefore, a sym- 
metry different from that of 11(d), transitions from 27 to 77 can lead 
only to c if AJ = 0, while for AJ = ± 1 they must lead to d (Figure 
56). Thus, either a singlet or a doublet progression, but never a triplet 
series, is produced by absorption of monochromatic light (example: 
the green to orange Na 2 resonance spectra). 



s*j; 



j, J '+< + -- 



J, 



4+i . 



J,., 






I V' 'ff 



V 

c 4 



c 3 

C Z*v" r 

c I 

*c '?* 



Fig. 56. Doublet and singlet progressions for 27 -s- 77 transition. 



The band spectra due to transitions between other electronic 
terms like 77 -> 77, 77^ A show (J-branches as well as P- and 7?-branches, 
although the intensity of the former is relatively low ; they are of little 
importance for the fluorescence spectra of the diatomic gases which 
have been investigated so far. 

46. Shape of the Potential Curves. The term diagram of Figure 54 
gives an accurate picture of the lines occurring in a resonance spectrum 
which results from the transition from a level T'v' to the various 
levels v" of the electronic ground state. The scheme, however, does 
not give any indications concerning the relative intensities of the 
individual lines. These can be obtained by using potential curves in- 
stead of the level schemes for the representation of the electronic states 
and by applying the so-called Franck-Condon principle. 

In Figure 57 the abscissa measures again the distance r between 
two atomic nuclei, and the ordinate the sum U = T + V of the 
electronic excitation energy and of the potential energy of the nuclear 



146 



DIATOMIC GASES AND VAPORS 



configuration, while the molecular rotation is neglected. If the nuclei 
are at infinite distance from each other V is zero and, as in Figure 36, 
49 and 50, the vertical distance between the curves N and A is equal 
to the electronic energy of one of the atoms in an excited state. If (in 
contradistinction to the assumption on which the curves of Figures 



\ 

8 I 














/i 


f 




J 

r 


I /] 


v ,' 


. 








'_ . 


t 

I 

*. 1 

D"\ 

1 
1__ 

1 

i 

1 — 

1 

c 1--. 


— t4 

y u -o 




x 

* 



Fig. 57. Potential curves for the fluorescence of a diatomic 
molecule. 



36 and 50 were based) an attractive force exists between the two 
atomic nuclei so that a stable molecule can be formed, U assumes 
negative values if the two unexcited atoms approach each other 
adiabatically. At very small distances between the two nuclei the 
repulsive force prevails, causing a steep rise of the curve. The minimum 
of U corresponds to the equilibrium of the nonvibrating molecule at 
the nuclear distance r . The vertical distance between this point and 
the horizontal branch of the curve at great values of r corresponds to 
the work which must be applied to separate the nonvibrating molecule 
into two single atoms, or to the heat of dissociation D. For the sake of 
simplicity, the zero axis of energy is shifted in Figure 57 so that all 



FRANCK-CONDON PRINCIPLE 147 

energies which occur (especially the energy of the nonvibrating un- 
excited molecule) assume positive values. 

The function representing the potential energy of diatomic mole- 
cules in its relation to the interatomic distance has not yet be.en worked 
out in a generally valid form which can be numerically evaluated. 
The best approximation is probably still obtained by Morse's semi- 
empirical equation: 

U(r) = JE^ + JD{1 — e-oe«) (46a) 

in which 



a = 2nco e c 



y 2D 



and q = r — r , the deviation from the equilibrium position. If, in 
Equation (34), the coefficient wx is very small, the oscillating molecule 
can be treated, in first approximation, as a classical harmonic oscillator, 
as long as the amplitudes are not too large, and its potential energy can 
be represented by the equation : 

U(r) = E^ + bg 2 (46b) 

Under these conditions, the potential curve becomes a symmetrical 
hyperbola. 

Since the vibrational energy of the molecule is quantized and 
since the energy is completely potential at the turning points of the 
oscillation, U can assume at these points only definite values which 
are determined by Equation (34) and which are indicated in Figure 57 
by dotted horizontal lines. For a given value of the vibrational quantum 
number v, U oscillates according to the potential curve between the 
near and the far turning point. For v = 0, the vibrational energy of the 
molecule does not vanish, but it becomes 1 f 2 w e — 1 / i a> e x e [Equation 
(35) ] ; even the so-called nonoscillating state of the molecule does not 
correspond exactly to the lowest point on the potential curve, but to 
the undermost horizontal line in the diagram. 

47. Franck-Condon (F.C.) Principle. If Franck's idea, according to 
which the position and the momentum of the nuclei cannot change 
appreciably during an electronic transition (cf. Section 35), is applied 
to the processes occurring in a diatomic molecule, only those tran- 
sitions between the potential curves A and N have a reasonable pro- 
bability which correspond to vertical arrows in the diagram. In the 
case represented by Figure 57, for instance, transitions from the 
ground state with v" = can lead only to vibrational levels of the 



148 



DIATOMIC GASES AND VAPORS 



excited state A between v' = and v' = v x (a t and c in Figure 57). 
The molecules stay longest in the neighborhood of the turning points 
and, therefore, those transitions which are indicated by the arrows a t 
and # 2 have the greatest probability in the process of re-emission. 

These considerations, based by Franck on plausible assump- 
tions, later received a precise quantum-mechanical treatment by 
Condon and since then have been known as the Franck-Condon prin- 
ciple. The transition probability between the vibrational levels v' 
and v" of two electronic states T' and T" is defined, within the approxi- 
mation of Equation (32a), by: 



W = C 



fv'Mv" 



*(v") dr 



(47) 



v°0 



*l>'{v') and <fi"{v") are the eigenfunctions characterizing the vibrational 
states v' and v° of the electronic states T' and T", respectively. C is a 

constant which contains the probability 
of the electronic transition T' -+T", 
supposed to be independent of v' and 
v". In Figure 58 the first eigenfunctions 
of a harmonic oscillator are reproduced 
f or v = 0, 1 , 2 . . . ; in general, the eigen- 
functions have a number of nodes and 
antinodes and the probability of a 
certain transition, as defined by the 
integral of Equation (47), depends to a 
great extent on the relative position of 
the nodes and antinodes of the two 
functions tfj' and xj>" . For greater values 
of v, the number and height of anti- 
nodes near the turning points increase ; 
this is the reason why the first for- 
mulation of Franck's principle yielded 
useful results. For values of v near 
zero, however, the deviations become considerable. 

In principle, the eigenfunctions can be derived for each case from 
the potential curves, but the calculation — at least as far as the 
analysis of resonance spectra is concerned — has been carried through 
only for a very few examples. Even there, the problem was greatly 
simplified by the assumption that the oscillations could be considered 
as purely harmonic in both electronic states (Sections 53 and 60). The 




tf=2 



t/=3 



V=4 



Fig. 58. Eigenfunctions of the 

five lowest vibrational states 

of a harmonic oscillator. 



FRANCK-CONDON PRINCIPLE 



149 



application of the same method to the analysis of the resonance spectra 
of iodine lead to entirely erroneous results, probably because one or 
several erroneous assumptions were introduced into the calculation 
{24,175,1026). 

For- obtaining at least qualitative results, it is thus necessary to 
use the F.C. principle in its original formulation. It is easily realized 
that the type of the absorption spectrum, as well as the possibility 
of exciting fluorescence, depends not only on the shape but also on 
the relative position of the two potential curves, which represent 
the 2 combining electronic states. Also, the unexcited molecules are, 
at not too high temperatures, in low vibrational states (v" = or 
v" = 1) and, on the other hand, a transition to a point higher than 
the level of dissociation of an electronic state leads to dissociation of the 
molecule. Since the kinetic energy of the separating atoms (corres- 
ponding to the surplus energy 8 in the figure) is no longer quantized, 
all points on the potential curve above D' are virtual turning points 
and, therefore, absorption or emission processes leading to such points 
do not produce separate lines but continuous bands. If transitions from 
the lowest vibrational level of N into discrete levels of A are most prob- 
able on the basis of these considerations, the major part of the ab- 
sjx>rtion spectrum will show bands with fine structure, and, in the 
absence of perturbations, the return from the excited state A to the 
ground state N will occur with the emission of fluorescence. Examples 
of this behavior are provided by the first absorption band systems of I 2 
and Na 2 . If the values of r" and r' are nearly equal and if the two 
potential curves between which the transitions take place have nearly 
the same shape, transitions with Av = are the most frequent. In the 
limiting case, the resonance spectrum would consist of only one strong 
line, possibly accompanied by a few others 
of rapidly decreasing intensities, and 
fluorescence would be excited practically 
only by the absorption of lines fulfilling 
the conditionals = 0.1f,on the other hand, 
r" and r differ widely, the resonance 
spectrum produced by the absorption of 
a line has two maxima of intensity, 
corresponding to transitions from the 
near and from the far turning points of 

the excited state. The second of these F * 59 Potential curves 

01 a molecule with a con- 
transitions can correspond to the conti- tinuous band prevailing in 
nuous part of the emission spectrum. If, the absorption spectrum. 




150 DIATOMIC GASES AND VAPORS 

finally, transitions by which the molecule is transferred into the 
region of continuous energy of the state A have the greatest probabi- 
lity (Figure 59), or if only such transitions can occur, the part of the 
absorption spectrum showing fine structure is weak or completely 
missing and irradiation witht monochromatic light produces no 
fluorescence because every absorption process leads to the dissociation 
of the absorbing molecule. 

If transitions from an excited quantized state bring the mole- 
cule, according to the F.C. principle, to the part of a potential curve 
corresponding to a non-quantized state, the emission spectrum does 
not consist of separate lines but of a continuous band. Such emission 
bands must occur if the second state is characterized by a repulsion 
curve ; they occur, also, if the transition leads to a point of an attraction 
curve lying either, for r < r Q , above the dissociation energy level or, 
for r > r , on the almost horizontal branch which corresponds to a 
complete separation of the nuclei. If (as, for instance, in the last case) 
the potential curve of the nonquantized state has a very small slope, 
the continuous band can exhibit a sequence of maxima and minima, 
so-called "fluctuations." The spacing of these maxima is of the order 
of magnitude of AG(v') or of a>', because the energy of the lower elec- 
tronic state is practically independent of the intranuclear distance, while 
the vibrational levels of the upper electronic state are separated by in- 
tervals AG[v') . However, the spacing of the fluctuations may decrease in 
the direction of longer or shorter wavelengths according to the slope of 
the lower potential curve: "pseudoconvergence" of the fluctuations. 

Analogous conditions can cause the inverse effect, the occurrence 
of fluctuation bands in the absorption spectrum, if a transition leads 
from a quantized electronic ground state to a nearly horizontal branch 
of the potential curve representing a nonquantized excited state. By- 
absorption of light in such fluctuation bands, fluorescence cannot be 
excited, exactly as no fluorescence is excited by absorption in normal 
continuous bands. 

Apart from the transition probabilities, the intensity of an emission 
line depends, of course, on the number of molecules which are in the 
state from which the line originates. The initial state is the same for 
all lines of a resonance spectrum excited by the same strictly mono- 
chromatic line; therefore, their relative intensities are independent 
of the number of excited molecules. This is no longer true if the ab- 
sorbing molecules are raised to different levels of rotation and oscil- 
lation by irradiation with a primary line which is broad enough to 
cover several neighboring lines of an absorption band. 



THE VISIBLE BAND SYSTEM OF I 2 151 

B. Fluorescence of the Halogen Vapors 

48. The Visible Band System of I 2 . The fluorescence spectrum of 
iodine vapor is treated here, without regard to any systematic order, 
as a first example because it was the first which has been investigated 
thoroughly, and because it provides the possibility of discussing almost 
every theoretical consideration mentioned in the last sections. 

In the visible part of the spectrum iodine vapor, saturated at 
room temperature, shows an absorption band system which consists of 
numerous bands partially overlapping each other. By means of a 
powerful grating, these bands are resolved into a very large number 
of fine lines so that, for example, 100 individual lines can be counted 
in the interval between the two D-lines . Until recently, the band system 
which stretches from about 5000 to 7000A was ascribed to a transition 
1 E*r- 1 i7. On the basis of theoretical considerations, Mulliken as- 
certained that the upper state is a 3 77 -state which is split into two 
levels by "A -doubling" ; these two levels behave almost like in- 
dependent ^-states and only one of them (designated by Mulliken as 
*0+ combines with the ground state. Thus, practically all conclusions 
arrived at from the older assumption are preserved as correct (1092). 

Lommel was the first to observe that when iodine vapor was 
irradiated with sunlight, it emitted a strong greenish-yellow fluo- 
rescence which, viewed through a spectroscope, looked like the reversal 
of the absorption spectrum. The fine structure of these fluorescence 
bands and the occurrence of resonance spectra under monochromatic 
excitation were later discovered by R. W. Wood (949,1862). 

The resonance spectrum which is produced by irradiating iodine 
vapor with the green mercury line 5461 A has been investigated in 
every detail (760,820,950,1005,133711,1870,1875,1877,1883). If this line 
originates from a hot mercury arc, it covers at least nine iodine ab- 
sorption lines. However, if the mercury arc lamp is water cooled, the 
green line becomes sufficiently sharp to coincide with a single iodine 
line and, thus, to excite only molecules of one definite initial state. A 
part of the resonance spectrum obtained under these conditions by 
Wood and Kimura is reproduced in Figure 60 and 61. Photograms 
obtained by means of an interferometer of high resolving power 
prove that the doublet components of this spectrum are devoid of any 
further structure {1907) . 

Wood derived empirically the law governing the spacing of the 
lines in the spectrum ; later it was worked out in detail on the basis of 



152 



DIATOMIC GASES AND VAPORS 





Fig. 60. Resonance spectrum of I 2 , order 1-3. 







Fig. 61. Resonance spectrum of I 2 , order 15-22. 



the theory which had been developed in the meantime. According to 
Rank, who improved the precision of the measurements and whose 
figures are listed in Table 23, the progression of the main lines of the 
doublets is represented with high accuracy by the formula : 



v — 18307.50 — 213.79771;" + 0.614045»" a 
0.00001 866i>" 4 

The doublet separation is given by : 

dv = 5.168— 0.194y" 



0.000931961?;" 3 + 



(48a) 



(48b) 



and the molecular constants for the iodine molecule derived from 
Equation (48a) are: <J' e = 214.57; x" e w e = 0.6127; y e <*\ = 0.000895; 
2> e " = 0.0000187; B" e = 0.00375; a" = 0.000191. 

The resonance spectrum has been extended by Oldenberg, Loomis, 
and Rank as far as to the 39th member at 9097A by means of infrared 
sensitized plates (953,1165,1337a). It does not contain any "anti- 
Stokes" lines (with wavelengths shorter than that of the exciting 
line). Hence, the exciting line is absorbed by molecules in the lowest 
vibrational state (v" = 0). The vibrational quantum number of the 
excited state is v' = 26 as Kemble and Witmer, and Loomis, proved 
by a very thorough analysis of the complete absorption and fluo- 
rescence spectrum. Accordingly, the i?-line is produced by the tran- 
sition v' -> v" = 26' -> 0", and the following lines by 26' -> 1 ", 26' -* 2", 
etc. For the doublets with order numbers beyond 27, the vibrational 
energy increases in the emission process (26' -> 27", 26' -* 28", etc.*) 
(760,950). 

* The symbols 26", 27', etc., are used for v" = 26,i;' = 27. etc.). 



THE VISIBLE BAND SYSTEM OF I 2 



153 



Table 23 
Resonance Spectrum of Iodine Vapor Excited by the Green 

Mercury Line 5460. 724A 
(Wavelengths A in A in atmospheric air; wave numbers v in cm -1 reduced 

to vacuum) 



v" 


X 


V 


v" 


X 


' 


V* 


A 


V 





5459.2 


18312.68 


13 


6394.4 


15634.49 


26 


missing 




5460.7 


18307.50 




6396.4 


15629.58 








1 


5525.1 


18094.30 


14 


missing 


27 


7683.7 


13011.0 




5526.6 


18089.17 










7686.6 


13006.0 


2 


m 


ssing 


15 


6558.8 
6560.9 


15242.6 
15237.7 


28 


missing 


3 


5657.2 


17671.66 


16 


6643.2 


15048.9 


29 


7896.8 


12659.9 




5658.9 


17666.54 




6645.2 


15044.3 




7899.4 


12655.7 


4 


5725.1 


17462.20 


17 


6729.3 


14856.4 


30 


8006.4 


12486.5 




5726.7 


17457.09 




6731.4 


14851.6 




8009.5 


12481.7 


5 


5794.2 


17253.9 


18 


6816.8 


14665.7 


31 


missing 




5795.9 


17248.8 




6819.0 


14660.8 








6 


5864.5 
5866.2 


17047.03 
17041.98 


19 


p 


? 


32 


8231.9 
8234.9 


12144.6 
12140.3 


7 


m 


ssing 


20 


6997.1 
6-999.4 


14287.8 
14282.8 


33 


m 


ssing 


8 


6009.1 
6010.9 


16636.95 
16631.95 


21 


m 


ssing 


34 


8465.4 
8468.6 


11809.5 
11805.1 


9 


missing 


22 


7184.3 


13915.5 


35 


8585.6 


11644.2 










7188.7 


13910.7 




8588.7 


11640.0 


10 


6159.0 


16232.03 


23 


7280.4 


13731.8 


36 


8707.4 


11481.4 




6160.9 


16227.05 




7282.9 


13727.0 




8710.3 


11476.9 


11 


6236.0 
6237.9 


16031.55 
16026.59 


24 


m 


ssing 


37 


8831.8 
8835.1 


11319.6 
11315.4 


12 


m 


issing 


25 


7478.4 
7480.9 


13368.2 
13363.8 


38 
39 


m 

9087.3 
9090.6 


ssing 

11001.4 
10997.4 



Pringsheim 6 



154 DIATOMIC GASES AND VAPORS 

The intensity distribution of the observed lines is not only very 
irregular, but some lines, for instance the members 2, 7, 9 in Table 23, 
seem to be missing altogether. The theoretical explanation of this 
phenomenon, which occurs more or less pronouncedly in all resonance 
spectra, has already been given in the preceding section. For a reason 
which is not obvious, the intensity maximum of most resonance 
spectra lies near the R-line or in this line itself. It is probably due to 
a tendency to investigate the most brilliant fluorescence spectra. These 
are excited by the absorption of lines which are strong in the absorption 
spectrum and thus correspond to a great transition probability, 
v'<-v". The transition probability v'^-v" and the intensity of the 
.R-line in the resonance spectrum are, therefore, also great. 

If the fluorescence of iodine vapor is excited by the green line 
from a hot mercury arc, the other absorption lines covered by the 
mercury line contribute to the excitation, and molecules in different 
levels of the ground state are raised into different vibrational and 
rotational levels of the excited state. From every one of these a com- 
plete series of doublets originates. For most of the series observed by 
Wood, it has been possible to determine the location of the R-line in 
the Fortrat diagram characterizing the bands. Three more series 
correspond to the transition 26' ^ 0" in the absorption process, but 
with different rotational quantum numbers so that two of the four 
iMines belong to the P-branch and two to the i?-branch of the Fortrat 
parabola 26 -0". The differences between the /-values of these lines 
are not large (compare Table 24 and Figure 62) and the separations 
of the corresponding doublet components are nearly the same, ac- 
cording to Equation (42). For the first two doublets, the companion 
lines lie on the side of greater wavelengths ; for the other two, on the 
short wavelength side of the main line ($50,951,1875,1877,1883). 

Among the other I 2 -absorption lines covered by the broadened 
green mercury line, five correspond to transitions from the "vi- 
brationless" ground state to higher vibrational levels of the excited 
state; they belong to the bands 27'-0", 28'-0", and 29'-0". The "zero 
lines" of these bands (with/" = 0) have much higher frequencies than 
the exciting mercury line, which is close to the zero line of the band 
26'-0". A line belonging to a band with a greater v' can coincide with 
the broadened mercury line only if the rotational quantum number/" 
has a relatively high value [compare Equation (38)]. Under these 
conditions the doublet separation, which is proportional to /", be- 
comes much larger. The transitions assumed by Loomis for the 
various iMines excited by the green mercury line are listed in Table 24. 



THE VISIBLE BAND SYSTEM OF I 2 



155 



Table 24 

Doublets in the Resonance Spectra of Iodine Vapor Excited by 

the Green Mercury Line 



v" 


v' 


}* 


r 


Branch to which 

the 2? -line 

belongs 


5v 

Frequency difference 

of doublet components 

(cm- 1 ) 


Designation 
in diagram 






28 


29 


P 


4.3 


0* 






29 


30 


P 


4.4 








26 


34 


33 


R 


—5.0 


0' 






35 


34 


R 


—5.2 


0*' 





27 


80 


81 


P 


12.0 


1 






85 


84 


R 


—12.73 


1' 





28 


108 


109 


P 


16.13 


2 





29 


129 


130 


P 


19.26 


3 






134 


133 


R 


—19.9 


3' 






45 


46 


P 


7.6 


4 


1 


29 


50 


49 


R 


—6.6 


4' 






51 


50 


R 


—8.3 


4*' 



v'-u" 




18290 



18300 



l 18310 
Hg5461 Satellite 
V *■ 



Fig. 62. Fortrat diagram for the doublets of zero order excited in 
1 2 - vapor by the green Hg-line. 



1 56 DIATOMIC GASES AND VAPORS 

Figure 62 shows the complete Fortrat parabola for the band 26-0": 
the curves for the other bands may be continued on the right-hand 
side down to the point where they cross the 0-axis. The ordinates are 
the values of /'; they are the same for either component of every 
doublet. The distances separating the components of a doublet are 
indicated by a horizontal line joining the i?-line and its companion. 

The doublet separations S v decrease in every progression linearly 
with increasing v", in agreement with Equation (42). Finally, it 
follows from Equation (43b) that if several series have one line in 
common (for instance, the various series excited by the green mercury 
line), all principal doublet components of these series (but not the 
companion lines) must also very nearly coincide, forming apparently 
a single series, if the analyzing spectroscope has a small resolving 
power. However, since each series belongs to another rotational 
quantum number J', the separation becomes appreciable for higher 
values of v", where the last term in Equation (42) (4/W) can no 
longer be neglected. This also is in complete agreement with Wood's 
experimental results. 

In all iodine resonance spectra which are excited by the green 
mercury line and have no anti-Stokes lines, the intensity distribution 
is almost identical and, in particular, the same orders which are 
marked as missing in Table 22 are missing in every one of these series. 
This is not a self-evident conclusion to be drawn from any of the 
theoretical considerations put forward in the foregoing sections, since 
some of the series originate from different, although closely adjacent, 
vibrational levels. However, because of the relatively high values of 
v', the eigenfunctions for all these levels have a great number of 
maxima near the turning points, so that the transition probabilities 
for the series depend essentially on the eigenfunctions of the lower 
states determined by v". (This is not the case for other resonance 
spectra — for instance, those of Na^. 

In resonance spectra having an anti-Stokes member (v" = 1), 
lines appear with wavelengths which are missing in the progressions 
corresponding to v" = 0. If the emission of a line of a given wavelength 
leads to a vibrational level v" in one of these latter progressions, the 
emission of a line with almost the same wavelength will lead to the 
level v" + 1 in a series containing an anti-Stokes member. Thus, the 
spectral location of the "missing line" v" = 2 will now be occupied by 
the line v" = 3 and the same holds for the other missing lines. Because 
they are not hidden by the much stronger lines of the series 0*-3 in 
Table 24, Loomis was able to determine their exact frequencies in 



THE VISIBLE BRND SYSTEM OF I 2 157 

spite of their low intensities. Whether in the progressions 4 (Table 24) 
the lines corresponding to v" = 2, 7, 9 . . . are also missing cannot be 
decided because of their coincidence with the lines corresponding to 
v" = 1, 6, 8 ... of the progressions without anti-Stokes members.* 

The high values of /" occurring in Table 24 may seem to be 
remarkable; they suggest that unexcited iodine vapor contains con- 
siderable numbers of molecules with rotational quantum numbers up 
to 135. This is possible because of the relatively large moment of 
inertia of iodine molecules, which can be derived from the constant 
B according to the relation : B = hj8-n 2 I. The analysis of the resonance 
spectra provides the value of B = 0.037. Thus, I = 8- lO" 38 g cm 2 
and the quantum number /" = 135 corresponds to the rotational 
energy F = h-B-J(J + 1) = 0.08 eV; this is about four times the 
average rotational energy at room temperature, so that an appreciable 
fraction of the molecules occupies rotational levels with those high 
quantum numbers. 

On the other hand, the vibrational energy of the molecules is so 
large even for small values of v" that most of the unexcited molecules 
are in the nonvibrating state and comparatively few in the first 
quantum state of vibration. Accordingly, resonance series without an 
anti-Stokes member, or with only one such member, have the greatest 
intensity. A series with a second anti-Stokes member is also stimulated 
by absorption of the broad green mercury line, but it is very weak and 
it has not been possible, so far, to assign definite order numbers to 
its lines. However, if iodine vapor of constant density is heated to 
300° C, the intensity of this series increases very much in comparison 
to the intensity of the other series. Under conditions such as these, it 
is even possible to obtain a fourth and a fifth anti-Stokes line which 
belong to still other progressions excited by the green mercury line. 
An increase of temperature does not alter the intensity distribution 
within a homogeneous resonance spectrum, but it will alter the relative 
intensities of whole series, because the number of molecules in the 
corresponding initial states v"j" increases or decreases. For the same 
reason, only the anti-Stokes and the first positive members of a pro- 
gression are absorbed, if the fluorescence light produced by a mono- 
chromatic line is viewed through a layer of iodine vapor at room 
temperature. The lines of greater wavelengths (v" > 4) remain practi- 

* In resonance spectra without anti-Stokes members, Wood's original 
order numbers p coincide with the "rational" numbers v " . For series with one, 
two or more anti-Stokes members, they differ by 1, 2 . . . and negative values 
of p have to be introduced for the anti-Stokes members. 

Pringsheim 6* 



158 



DIATOMIC GASES AND VAPORS 



cally unaffected and, thus, the color of the fluorescence is shifted verv 
appreciably towards the red. While there are practically no molecules 
with more than four vibrational quanta in the unexcited vapor at 
20° C, the lines of higher order, at least up to v" = 6, are weakened to 
an increasing degree if the temperature of the absorbing vapor is 
raised to 300° C (1276). 

If the fluorescence of iodine vapor is excited by the absorption of 
white light, the resulting emission spectrum is very similar to the 
absorption spectrum, but it contains a great many more lines, for 
almost all absorption processes start from the levels v" = and 
v" = 1, while the emission processes end partly at levels with much 
higher values of v". Therefore, the center of gravity of the total fluo- 
rescence spectrum is displaced towards longer wavelengths, compared 
to that of the absorption spectrum ("Stokes' law") (1278,187$). 

Argabiceanu, who excited the fluorescence of iodine vapor by 
means of a mercury arc emitting a very narrow green line, obtained a 
resonance spectrum with as many as six anti-Stokes members. The 
excitation of this series corresponds, according to his calculations, to 
the transitions 32' <- 2", 35' <- 3", 39' «- 4", and 43' «- 5". Since these 
bands are completely missing in the absorption spectrum, Argabiceanu 
believes that the occurrence of the anti-Stokes lines can be explained 
by a "quantum-mechanical resonance phenomenon" (24). It may 
happen that because of the shape of the potential curves the trans- 
ition 43' -> 1" has, in a special 
case, a much greater probability 
than the transition 43'-*-5", so 
that the fourth anti-Stokes line 
is much brighter than the iWine 
in the progression which is ex- 
cited by the absorption process 
43' ■*- 5". However, if this process 
is induced at all by irradiating 
the vapor with the green mercury 
line, the unexcited vapor must, 
under all circumstances, contain 
molecules in the vibrational state 
v" = 5. If the corresponding band 
seems to be absent in the ab- 
sorption spectrum, it proves only 
that it is, in general, much easier 
to find isolated weak emission 




Cd Excitation 



Cu Excitation 



Hg Excitation 



Na Excitation 



' O in ffi — 10 0> K} 

' O J, — <B 00 ID 01 

_•— — oj-jt tor-Co 

in in in io in in in in 



Fig. 63. Resonance spectra of I« 
excited bv various lines. 



THE VISIBLE BAND SYSTEM OF I 2 



159 



lines than to find a weak absorption band on a background which is 
covered by many other, much stronger absorption bands (24) . 

Resonance spectra produced in the visible band system of iodine 
vapor by the absorption of the two yellow mercury lines and by 
several zinc, cadmium, and sodium lines have also been investigated, 
although less thoroughly (Figure 63). The resonance series excited by 
the yellow mercury lines show several anti-Stokes members and, 
while at room temperature their intensities are low compared with the 
fluorescence excited by the green mercury line, they increase con- 
siderably with increasing temperature* (1276,1786a). 

Table 25 

d State 01 

Various Exciting Lines 



Light 
source 


Wavelength in A 


v" 


v' 


/' 


Na 


5893 


2 


17 


30 






1 


15 


47 


Hg 


5791 


2 


19 


44; 37 and 38 






1 


17 


61 and 54 






1 


20 


169 









15? 


72 


Hg 


5770 


2 


20 


68 






1 


18 


80 









16 


93 and 86 


Hg 


5461 





26 


35; 34; 29 and 28 









27 


85 and 80 









28 


108 









29 


134 and 129 






1 


29 


51; 50 and 45 


Cd 


5086 





50 


8 









51 


43 



As far as they are known, the quantum numbers corresponding 
to the various resonance series are collected in Table 25. Each of the 
spectra is represented satisfactorily, by Equation (48) which, originally, 
had been derived only for the resonance spectrum of Table 23. A 

* The yellow Hg-lines cover 10 and 12 lines, respectively, in the iodine 
absorption spectrum. Hence, the corresponding resonance spectra do not consist 
of doublets, but of complicated groups of lines. 



160 



DIATOMIC GASES AND VAPORS 



different value of v must, of course, be inserted into the equation for 
every series. 

If the resonance series which are produced by absorption of light 
in various parts of the band system are compared (Table 26), it is 
found that the longer the wavelength of the exciting light, the larger is 
the average number of anti-Stokes lines. This is due to the fact that 
the bands near the violet end of the system originate exclusively from 
the vibrationless level of the ground state (v" = 0), while with in- 
creasing wavelength of the absorption bands the higher vibrational 
levels come more and more into play. Because every exciting line 
covers more than one absorption line, only average numbers can be 
listed. Thus, the line 5461A has been shown to excite not only several 
series without anti-Stokes lines, but also series with one to six anti- 
Stokes members. The line 5218A, on the other hand, excites not a 
single series with an anti-Stokes line. 

If the vapor density is kept constant, the yield of the iodine fluo- 



Table 26 

Resonance Spectra of Iodine Vapor Excited by 
Monochromatic Light 





(Wavelengths in A; 


estimated relative intensities 


in parentheses) 


Exciting 
line 


5893 


5791 


5770 


5461 


5218 


5086 


1900 


—5 


? ( 0) 

















1860( 1) 


—4 


5621 ( 9) 


— 


— 


— 


— 


— 


— 


—3 


5686( 9) 


5590( 0) 


5570( 0) 


— 


— 


— 


1875( 1) 


—2 


5749(10) 


5652( 9) 


5632( 5) 


5350( 2) 


— 


— 


— 


— 1 


5816(10) 


5720(16) 


5700(13) 


5405(15) 


— 


5027( 0) 


1892( 2) 





5893(15) 


5791(20) 


5770(20) 


5461(10) 


5218(15) 


5086(15) 


1900(10) 


1 


5972( 8) 


5863(12) 


5842(16) 


5526( 2) 


5278( 6) 


5153( 6) 


1907( 8) 


2 


6046( 7) 


5935(10) 


4911( 7) 


5605( 9) 


5338(10) 


5192( 3) 


1915(10) 


3 


6126( 4) 


6012(?) 


5988( 5) 


5659( 4) 


5393( 4) 


5344( 6) 


1922(10) 


4 


6205( 5) 


6086 


6663 


5726( 4) 


5455( 6) 


— 


1930(10) 


5 


6295( 5) 


6164 


6140 


5795( 7) 


5514( 2) 


5353( 8) 


1938(12) 


6 


? ( 1) 


6245 


6215 


5866( 1) 


5577( 5) 


— 


1946(11) 


7 


6462( 2) 


6324 


6298 


5950( 1) 


5636( 2) 


5477( 8) 


1954(12) 


8 


— 


6405 


— 


6011( 0) 


5703( 4) 


— 


1961(11) 


9 


— 


6494 


— 


6095( 0) 


5770( 5) 


5602( 5) 


1969(13) 


10 


— 


— 


— 


— 


5846( 5) 


5672( 0) 


1977(11) 


11 


— 


— 


— 


— 


5922( 2) 


5725( 0) 


1985(13) 


12 


— 


— 


— 


— 


5991 ( 1) 


— 


1993(12) 


13 


— 


— 


— 


— 


6078( 0) 


5850( 1) 


2002(12) 


14 


— 




~ 






_ 


2010(14) 



ULTRAVIOLET RESONANCE SPECTRA OF IODINE VAPOR 161 

rescence is practically independent of the temperature. It begins to 
decrease only at the temperature at which the dissociation of the mole- 
cules becomes noticeable (858). 

At 4990A, the band system converges and merges into a region of 
continuous absorption, the intensity of which drops rather rapidly with 
decreasing wavelength. Absorption of light in this part of the 
spectrum causes no fluorescence, but the optical dissociation of the 
molecules into a normal and an excited atom, according to the 
equation : 

I t + kv+ I( 2 P 3/2 ) + I( 2 P l/2 ) + £kin (49) 

The theoretical prediction was corroborated experimentally by 
Turner, who observed, under these conditions, the appearance of 
atomic iodine lines in theabsorption spectrumof thevapor. The excited 
state ( 2 P 1/2 ) of the iodine atom is metastable, so that the dissociation 
process is not followed by the emission of an atomic fluorescence 

{I7I5)- 

49. Ultraviolet Resonance Spectra of Iodine Vapor. A second band 
system is observed at room temperature in the absorption spectrum of 
iodine vapor between 1 760 and 2000A. At greater vapor pressures and 
with temperatures increasing up to 1 100 C°, it can be followed to ca. 
3440A because of the increasing number of unexcited molecules in 
higher vibrational states. In the numerous resonance spectra which 
were obtained in this band system, the spacing A G between consecutive 
lines was found to be of the same order of magnitude as in the visible 
resonance spectra. Hence, the lower state into which the molecules are 
transferred by the emission of the u.v. bands is, again, the electronic 
ground state (332,1160,1787). 

The analysis of the u.v. band system is less complete by far than 
that of the visible bands. Almost all data referring to the upper state 
are missing. Cordes' assumption that it is a 1 Z'-state agrees with the 
observation that, as far as they are analyzed, the resonance series seem 
to consist of doublets. It follows, furthermore, from the investigation 
of the absorption and the fluorescence spectra that transitions with 
large Av have the greatest probability ; this means that the potential 
curve of the upper state must be shifted considerably with respect to 
that of the ground state (cf. curve C in Figure 64). Finally, the 
vibrational levels of the upper state have AG values less than half as 
large as those of the ground state and converge very slowly, corre- 
sponding to a very large heat of dissociation. 

At room temperature, fluorescence of appreciable intensity is 



162 



DIATOMIC GASES AND VAPORS 



excited only by lines of wavelengths below 2100A. Oldenberg, who 
discovered this fluorescence, obtained resonance spectra by irradiating 
the vapor with the mercury lines 1849 and 1943 A, the bismuth line 
1903A, and the zinc line 1900A. For only the last of these spectra .the 
wavelengths of the individual members, which were not resolved into 
doublets, have been published. They stretch from the fifth anti-Stokes 



-i 
cm 

60000 



40000 



20 000 




45000 




Fig. 64. Potential curves of the I 2 -molecule [after 
Curtis and Evans (234)]. 

member to the thirty-fifth member with a positive order number. 
Asagoe, and Kimura and Tonomura, have investigated, much more 
thoroughly, several resonance series which were produced by the 
iodine atomic lines 1830 and 1844A [29,777). These lines were excited 
by means of an electric discharge through a tube containing iodine 
vapor saturated at 0° C and were reabsorbed by the I 2 -molecules con- 
tained in the same tube. This method of fluorescence excitation, which 
the authors called "auto-resonance", is very efficient, since the pri- 
mary lines are produced in the same volume in which they excite the 
fluorescence and, moreover, all windows which might weaken the 
short-wavelength, u.v. primary light are avoided. A' disadvantage of 
the method is the attendant difficulty of deciding to what extent the 



ULTRAVIOLET RESONANCE SPECTRA OF IODINE VAPOR 163 

molecular emission is actually caused by the irradiation and not 
directly by the electric discharge or by collisions of the second kind. 
If, however, the emission spectrum consists only of a few i>"-pro- 
gressions out of the whole band system, the conclusion seems to be 
justified that excitation is caused by the absorption of a few mono- 
chromatic lines. 

One of the progressions (I in Table 27) originates from the line 
1830A, the other (II to V) from the line 1846A. (Several series below 
2000A excited by the atomic iodine lines 1783, 1799, and 1876A were 
also observed, but no numerical data are given). The spectrograms 
were obtained by means of a quartz spectograph of high dispersion and 
record no lines below 2055A, so that all members with v" < 31 are 
missing. On the other hand, series I stretches as far as to the 85th 
order and series II and V even to the 96th order. This enables the 
authors to evaluate the constants of the ground state of the la- 
molecule with an accuracy which they consider to be better than 
that obtained by using the data from the visible bands. Instead of 
Equation (48), they give the following equation for their resonance 
series : 

v = v — 214.328(t> + V 2 ) + 0.5805(1/ + V 2 ) 2 + 0.00198(w + 1 / i ) 3 

+ 0.0000124(1/ + V2) 4 (50) 

while the "constant of interaction" is a" = 0.000018 instead of 
0.000191 cm -1 . Table 27 contains the other data relating to these 
series ; 8 v is the doublet separation in the doublet of shortest wave- 
length observed in each series. The brackets following the J" values 
indicate whether the exciting line belongs to a P- or an i?-branch. It is 
impossible to derive the quantum numbers v' from these observations. 
Resonance series which are excited in I 2 -vapor by lines of wave- 
lengths larger than 2000A are very weak at room temperature, but 
attain great intensity when the vapor is heated ; the longer the wave- 
length of the exciting radiation, the higher the minimum temperature 
at which the corresponding resonance spectrum can be observed with 
appreciable intensity. These minimum temperatures T m are listed in 
the third row of Table 28. The fourth row of the same table shows- 
under AG(v" + x l^j, the distances of the first Stokes line from the ex- 
citing line ; the approximate values of the v"s are derived from these by 
means of Equation (48) . All observed series are described satisfactorily 
within the limits of experimental error by inserting appropriate values 
for v into this equation. The doublet nature of the spectra could be 
ascertained in only a few cases ; the analysis is difficult and, in general. 



164 



DIATOMIC GASES AND VAPORS 



Table 27 

Ultraviolet Resonance Spectra of Iodine Vapor Excited by 

"Auto-Resonance" 





I 


II 


ill 


IV 


V 


Exciting line (A) . 

/" 

(5 v (cm -1 ) . . 


1830 



90(7?) 

11.3 


1846 

2 

48(P) 

6.6 


1846 

2 

50(P) 

6.6 


1846 

2 
24(R) 

? 


1846 

2 
26(P) 

? 



Table 28 

Ultraviolet Resonance Spectra of Iodine Vapor Excited by Light 

of Wavelengths above 2000A 



Exciting line (A) . . 
Exciting line "(cnr -1 ) . . 


Zn 2026 
49342 


Zn 2062 
48481 


Zn 3239 
46758 


Cd 2265 
44136 


Cd 2288 
43693 


Hg 2537 
39409 


t,„ ( s q 

v" 


20 

(6) 
205 


20 

(7) 

204 


100 
9 

202 
188 


250 
13 

198 
176 


250 

14 

197 

177 


500 

25 

184 

146 


AG[v" + i/ 2 ) (cm- 1 ) a 
AG(v" -4- i/j) (cm- 1 ) b 



not quite certain, because each of the exciting lines covers a large 
number of iodine absorption lines and, therefore, every resonance 
spectrum is composed of several superimposed series. Since the spacing 
AG is somewhat different for the individual overlapping series, they 
become farther separated with increasing order number, so that they 
form an inextricable "maze of lines" ("Liniengewirr") at the long- 
wavelength end of each resonance spectrum, as shown in Oldenberg's 
first paper. The fact that the individual series stimulated by "auto- 
excitation" could be followed up to such high values of v" must have 
been due to the particularly favorable sharpness and spectral location 
of the exciting lines (332,624,1160). 

At temperatures about 200° C above T m (Table 28), all resonance 
spectra which are excited by primary lines of wavelength greater than 
2100A begin to show a second progression b with appreciably smaller 
spacing than that of the original series a. The corresponding values of 

AG{v" + V 2 ) are listed in the last 



row of Table 28, and a typical 
example is reproduced in Figure 
65. The greater the wavelength of 
the exciting line, the larger is the 
difference between series a and b. 
With further increasing tempera- 




Fig. 65. Double resonance spectrum 

excited in I 2 -vapor at 200° C (a) 

560° C (b) by Zn-line 2139A. 



MCLENNAN BANDS 165 

ture, the intensity of series b exceeds that of a. This phenomenon, 
which occurs neither in the u.v. resonance spectra excited by light 
of wavelengths below 2100A nor in those of the visible band system, 
has not yet found a theoretical explanation (332). 

Concerning the nuclear vibrational levels of the excited electronic 
state from which the various u.v. resonance spectra orginate, one can 
say only that if v' is assumed (as a limiting case) to be equal to zero for 
the series excited by the mercury line 2537A, v' must be at least equal 
to 140 for the series excited by the line 1890A. 

50. McLennan Bands. In addition to the resonance spectra 
described in the last section, absorption of light in the u.v. band 
system of iodine vapor causes the appearance of a sequence of partly 
broad, partly rather narrow bands and groups of bands in the fluo- 
rescence spectrum. These bands were discovered by McLennan and 
are frequently designated as "McLennan (or Mc) bands" (997). The 
mechanism of their emission can be explained only by assuming that 
some nonquantized molecular states take part in the process (Section 
46). Furthermore, most of the Mc bands are never observed in the ab- 
sorption spectrum, although their intensity in the fluorescence spec- 
trum, and also under electrical excitation, is often very great. It is, 
therefore, improbable that the lower state is the electronic ground state 
of the molecules, unless highly excited nuclear vibrational levels come 
into play. 

The fluorescence bands discovered by McLennan belong to 
several different types. A long regular sequence of fluctuations between 
2000 and 2500A, with a spacing A v~380 cm -1 , appears simultaneously 
with the resonance progressions, if the exciting lines have wavelengths 
smaller than 1900A so that vibrational levels with large v' are excited; 
they overlap the "maze of lines" into which the resonance seriesmerge. 
A discussion of the energy relations proves that the electronic state 
reached by the emission of these bands lies below the dissociation limit 
of the unexcited molecules where no nonquantized energy states 
exist. Therefore, the emission piocess must start from an upper state F 
(Figure 64) which is not quantized, or the potential curve of which has 
only a very shallow minimum ; and the molecules must be transferred 
to this state from the closely adjacent electronic level C which has been 
reached by the primary absorption of light. It is not possible to give an 
interpretation for the very large values of A v which are almost double 
the cu" g characterizing the ground state. [The interpretation of similar 
fluctuation bands in the fluorescence spectra of tellurium and selenium 
vapor seems to be much less uncertain (compare Figure 70) . ] 



166 



DIATOMIC GASES AND VAPORS 



The other types of Mc bands are excited by the absorption of all 
lines which coincide with parts of the u.v. band system of iodine vapor. 
They consist of a great number of symmetrical bands (half-width ~ 
130 cm" 1 ) which are distributed somewhat irregularly over the whole 
spectral region between 4700 and 2500A, and of several broader con- 
tinuous bands which are superimposed upon the former. Although the 
main aspect of the bands is the same for all exciting lines, the exact 
location of each individual band and its relative intensity varies ac- 
cording to the frequency of the primary light. The group of bands 
between 3150 and 3290A, which is marked as c in Figure 66 and which 
occurs in all Mc-band spectra, is particularly characteristic in this 
respect. 

The smaller the wavelength of the exciting light, the farther these 



a (4700 A) b c(3200A) rf(2500A) 

Fig. 66. McLennan bands in the u.v. fluorescence spectrum 
of I 2 excited by white light (Duschinsky and Pringsheim). 

Mc bands stretch into the u.v. Several attempts have been made to 
divide the bands into regular sequences, but none of these agrees com- 
pletely with the experimental results. In Figure 66 the bands are 
divided into four groups (a-d), an arrangement suggested by a super- 
ficial survey of the spectra and their dependence on the wavelength 
of the exciting light — but this, also, is rather arbitrary {254,333). 

It is difficult to decide whether the occurrence of all Mc bands is 
due to a single upper and several lower states, or to more than one 
upper state. It seems rather probable that the upper state of the 
emission processes is quantized and that the lower state is continuous 
and lies above the limit of dissociation of the normal iodine molecules. 
The energy of the excited molecules in the state F from which the 
emission originates must depend to a certain extent on the quantum 
number v' of the vibrational level which is reached directly by ab- 
sorption of the exciting line and from which the molecule passes over 
into F. 

The frequency intervals between these bands are, on the average, 
220 cm -1 and, thus, are of the same order as the nuclear vibration 
quantum w" of the unexcited molecule. However, it has already been 
mentioned that the ground state of I 2 cannot be the final level of the 
emission process. Using all known data about ultraviolet absorption 



FLUORESCENCE OF OTHER HALOGEN VAPORS 167 

spectra of iodine vapor, Cordes has tried to build up a complete term 
scheme for the I 2 -molecule and to interpret the mechanism of the Mc 
bands on the basis of this scheme. However, this interpretation does 
not agree with a part of the results obtained in other investigations. 

Several broader, apparently continuous bands are superimposed 
on the other bands in the fluorescence spectrum of iodine vapor which 
is excited by short wavelength u.v. The most conspicuous of these 
continua are located at 2520-2730, 3040-3210 (Y), 3360-3440 (X), 
4040-4320, and 4400-4630A. The bands Y and X may form a single 
system. Various mechanisms have been proposed for the production 
of some of these bands (electron affinity spectrum of the I 2 -molecule, 
recombination luminescence corresponding to the process I + I -> I 2 , 
etc), but none has been satisfactory. At temperatures above 900° C, 
Warren succeeded in extending the discontinuous absorption band 
system from 2000A up to 3440A, where it merged into the band X ; 
accordingly, he interpreted this band as the "dissociation continuum" 
belonging to the system (1161,1787,1788). 

According to Elliott, it is extremely doubtful whether any genuine 
continua exist in the fluorescence spectrum of iodine vapor. It had 
been previously observed that several of the continua are replaced by 
bands with a conspicuous, though complicated, structure when 
foreign gases are added to the iodine vapor, and Elliott suggests that 
in the spectrum of pure I 2 -vapor at low pressure this structure is 
obliterated only because too many vibrational and rotational levels of 
the excited electronic state take part in the emission process. However, 
this interpretation, also seems, to involve certain inconsistencies, as 
will be discussed in Section 64 (360) . 

51. Other Halogen Vapors. The potential curves of the excited 
states are much more displaced with respect to those of the ground 
states for the other halogen vapors, and, therefore, the discontinuous 
parts of their first absorption band systems are much weaker as 
compared with the adjoining continua. Furthermore, the probability 
of the intercombination transition 3 II+- 1 E producing these first ab- 
sorption band systems is much smaller for the lighter molecules than 
for those of iodine.* According to Rabinowitch and W. C. Wood, the 
ratio of the total absorption in the bands of I 2 , Br 2 , and Cl 2 is 
740:160:90. Thus, resonance spectra could be obtained only with 
much longer exposure in bromine vapor, and it has not been possible so 

* This corresponds to the behavior of the atomic spectra of Hg, Cd, and 
Zn, respectively, in which the intercombination lines become less intense with 
decreasing atomic weight. 



168 



DIATOMIC GASES AND VAPORS 



far to observe any resonance fluorescence in chlorine vapor. (Compare 
Section 93 for an indirect method of exciting fluorescence of Br 2 
and Cy (1318). 

According to R. W. Wood and to Dunoyer, a weak yellowish 
fluorescence can be excited in bromine vapor by white light. Plumley 
obtained complete doublet progressions by irradiating the vapor with 
the light from a mercury arc and using high intensity apparatus and 
exposures of many hours. The progressions originated from the two 
yellow and from the green mercury lines. The resonance spectrum 
stimulated by the green line was about 300 times weaker than that 
excited in iodine vapor under similar conditions. Even if the relatively 
narrow line from a cooled mercury lamp is used, five resonance series 
of unequal doublet separation are excited in bromine vapor. They are 
ascribed by Plumley to various combinations of the two isotopes Br 79 
and Br 81 . Table 29 gives the doublet separations Bv as positive or 
negative, respectively, according to whether the exciting line lies on 
a P-orai?-branch, sothatthe "companion lines" are displaced towards 
greater or smaller wavelengths. Series I is by far the strongest; it has 
no anti-Stokes member and can be followed up to the 17th member. 
However, the values of S v decrease so rapidly that the doublet could 
be resolved only in the first order. The series can be described by the 
equation (260a, 1243,1871) : 



18307.5 — 322.67-t/' + 1.15V 2 



(51) 



In a mixture of iodine and bromine vapor, IBr-moIecules are 
formed. No fluorescence belonging to these molecules is excited by 
visible light, but, on irradiating the vapor with light of wavelengths 
below 2000A, the emission of a large number of rather diffuse bands 
is obtained in the region extending from 2890 to 4850A. Although they 
exhibit a certain likeness to the Mc bands of pure iodine, the two 



Table 29 

Resonance Spectrum of Bromine Vapor Excited 
by the Mercury Line 5461A 



No. of series 


Isotopes 


v" 


v' 


J" 


dv (A) 


1 


79-81 





19 


6{R) 


— 3.0 


11 


81-81 


1 


23 


n(R) 


— 6.0 


in 


79-81 


1 


25 


64{P) 


20.5 


IV 


79-79 





21 


74(P) 


24.0 


V 


79-81 





21 


76(H) 


— 25.0 



VAPORS OF THE ALKALI METALS 169 

spectra do not coincide. Furthermore, the IBr-bands do not stretch 
nearly as far towards the u.v. as the Mc bands, and the resonance 
series observed in the short wavelength region of the iodine fluo- 
rescence spectrum are completely missing from the IBr-spectrum {387, 

954)- 

In a mixture of iodine and chlorine vapor, a new characteristic 
fluorescence could no more be obtained than in pure chlorine vapor. 
According to Cordes and Sponer, IC1 exhibits a band absorption 
spectrum stretching from 1910A toward smaller wavelengths, whereas 
the corresponding system of IBr reaches as far as 1974A. 

C. Vapors of the Alkali Metals 

52. Existence of Diatomic Molecules. Typical "resonance spectra" 
were observed for the first time by R. W. Wood in the fluorescence of 
sodium vapor. Wiedemann had found that, if sodium vapor of 
sufficient density was irradiated with sunlight, an intense green fluo- 
rescence occurred along the whole length of the exciting beam ; using 
a spectroscope, he was able to resolve the luminescence spectrum into 
a series of channeled bands in the green, and a second series of such 
bands in the orange and red. Besides, the D-lines occurred with high 
intensity in the spectrum. The absorption spectrum of the vapor 
showed bands of similar structure in the same region, apart from the 
well-known lines of the principal series of the sodium atom {1833). 
Wood analyzed these bands by means of a spectrograph of high 
resolving power and proved, furthermore, the existence of similar 
absorption bands in the neighborhood of the absorption lines of the 
sodium atom in the u.v. All these bands were at first ascribed to 
atomic sodium (i860). Only after Bohr's theory had provided the basis 
for a theoretical treatment of band spectra, were diatomic molecules 
recognized as the carriers of band absorption and emission in metal 
vapors, which before had always been regarded as monatomic* 

Dunoyer held the opinion that the bands in the fluorescence 
spectrum of sodium vapor were caused by an organic impurity and 
that they disappeared after careful purification of the metal, and he 
published experimental results which seemed to prove the validity of 
his hypothesis. Although the cause of these observations has never 

* Naj-molecules as the carriers of the band spectra were suggested for 
the first time in the author's "Fluorescent und Phosphorescent im Lichte der 
neueren Atomtheorie," Springer, Berlin, 1921. 



1 70 DIATOMIC GASES AND VAPORS 

been cleared up properly, they were certainly not correct. For the 
intensity of the bands is exactly the same, no matter whether the vapor 
is produced by distillation of the technical metal preserved under 
benzene, or by decomposing sodium azide in vacuo, or whether the 
sodium is introduced into the observation chamber by electrolysis 
through the glass (Figure 67d). A further proof for the production of 
the bands by Na 2 -molecules can be seen in the fact that bands of the 
same type are not only observed in the absorption and emission spectra 
of the other alkali metal vapors, but that a new band system occurs in 



ratamnnsM 



Fig. 67. Fluorescence spectra of diatomic alkali metal vapors. 
a : pure potassium, b : pure sodium, c: mixed potassium and 
sodium, d-.pnre sodium prepared by disintegration of NaN 3 



a mixture of sodium and potassium vapor. This system is missing from 
the spectra of the vapors of pure sodium and potassium and must, 
therefore, be ascribed to the formation of NaK-molecules. In mixtures 
of other alkali metal vapors similar characteristic band systems occur, 
but have been observed so far only in absorption spectra (3^,1283). 
(After these spectroscopic results had destroyed all doubt that 
diatomic molecules exist in the vapors of alkali metals, their presence 
was also proved by precision measurements of vapor pressures and by 
other methods). 

The fact that the molecular bands are closely adjacent to the 
atomic lines in these and many other -spectra is understood by the 
assumption that the potential curves of the ground state and the 
excited states are very nearly parallel over their whole length. 

53. Resonance Spectra of Na 2 . The narrow spacing of the lines in 
the absorption spectrum of the Na 2 -molecules has the effect that 
within a wide spectral range practically every line produced by the 
arcs or sparks between any metal electrodes covers one or several ab- 
sorption lines and, thus, is able to excite at least one resonance pro- 
gression. Every progression produced in this way is confined either to 
the blue-green or to the orange-red bands; they belong to two inde- 
pendent systems and originate from different excited electronic states. 
Wood used a great many light sources (electric discharge through the 



RESONANCE SPECTRA OF Na 2 



171 



vapors of Hg, Cd, Zn, Mg, Pb, Ag, Bi, Cu, Li, Na, and Ba, and, further- 
more, through hydrogen and helium) for the production of fluorescence 
in sodium vapor. In most instances he did not isolate individual 
primary lines, so that in many of his spectrograms several resonance 
series overlap one another. The spacing AG is approximately the same 
in all these series, and if the exciting light consists of a group of lines, 
this group is repeated over the whole fluorescence spectrum with only 
slight modifications. This, for instance, is the case for the excitation 
by the green Mg-triplet 5167.4, 5172.9, 5183.7A. The series due to the 
second of these lines is listed in Table 30. On the spectrograms, every 
line has a companion on either side corresponding to the two other 
triplet components. The figures of the last row of the table are calcu- 
lated according to the empirical formula {1860,1863,1868, 1904) : 



= 19329 — 142. 3p + 0.845-£ 2 {p = 0, ± 1, ± 2 



(52) 



Table 30 
Resonance Spectrum of Na 2 Excited by the Mg-LiNE 5172.9A 



p 


— 6 


— 5 


— 4 


— 3 


— 2 


— 1 


Wavelength (A) 
Wave number 


4946 


4948 


5022 


5060 


5098 


5136 


(observed) 
Wave number 


20219 


20064 


19912 


19763 


19615 


19470 


(calculated) . . 


20214 


20062 


19912 


19764 


19617 


19472 



P 





+ 1 


+ 2 


+ 3 


+ 4 


Wavelength (A) .... 
Wave number 

(observed) 

Wave number 

(calculated) 


5172.9 
19329 
19329 


5212 
19187 
19188 


5250 
19048 
19048 


528S 
18911 
18910 


5327 

18773 
18774 



Table 31 contains those of the numerous' resonance spectra pho- 
tographed by Wood and others in the blue-green system of Na 2 for 
which an unambiguous assignment to a certain exciting line is possible. 
The rule is again confirmed that with increasing wavelength of the 
exciting light, the number of anti-Stokes lines tends to increase. This 
number is, in general, larger than for the green resonance spectra of 
iodine vapor because the observations must be made at higher 
temperatures (frequently above 500° C), and also because the vibra- 
tional quantum of the ground state is smaller for Na 2 than for I 2 . 



172 



DIATOMIC GASES AND VAPOR 



(N- 



Table 31 
Resonance Spectra of Na 2 
number of anti-Stokes lines; N+ = number of Stokes lines) 



Exciting 


Zn 


c<s* 


Zn 


Ba 


Li 


Pb 


Cd* 


Cu 


Mg 


Mg 


Mg 


Ag 


Cu 


line (A) 


4722 


4800 


4811 


4934 


4971 


5006 


5086 


5133 


5157 


5173 


5184 


5209 


5218 


N~ 


1 








2? 


3 


2 


4 


7 


3 


6 


9 


7 


9 


N + 


7 


14 


6 


10 


6 


7 





6 


1 


4 


3 


3 


2 


v"t 


1 








1? 


3 


2 


4 


7 


7 


8? 


8 


10 


11 


v'f 


9 


5 


4 


P 


? 


3 





1 


1 


2 


2 


5 


4 



* Compare pages 147 and 215. 

t v" an d v ' not quite certain in several cases. 

In Table 32, the constants characterizing the ground state of Na 2 
and other diatomic alkali molecules are collected. By means of these 
constants, empirical Equation (52) can be transformed into the 
"rational" equation representing all resonance progressions of the 
blue-green Na 2 -band system [compare Equations (43) and (44), 
Section 44]. 

Table 32 

Constants Characterizing the Ground State 

of Diatomic Alkali Molecules 

[I: moment of inertia (1519)] 



Molecule 


m \ 


°>"e x e 


D"(eV) 


/ • 10 3 ° 


Na 2 


159.23 

123.29 

92.3 

81.99 


0.726 
0.40 

? 

0.08 


1.0 
0.62 
0.61 
0.45 


2.5 


KNa 


6.6 


K, 


18.4 











The values given under D" for the heat of dissociation cannot be 
determined with any accuracy from the resonance spectra by extra- 
polation. The exact calculation became possible only by the analysis of 
the complete band systems carried through by Loomis and his colla- 
borators. However, the task was considerably simplified by the 
previous investigation of the resonance spectra (9 52, g 56a). 

According to this analysis, the ground state of the Na 2 -molecule 
(and also that of the other alkali metal molecules) is characterized by 



RESONANCE SPECTRA OF ifa^ 



173 



the symbol J i7+ ; the excited state from which the emission of the blue- 
green band of Na 2 (and also the orange band of KNa and the red band 
of K 2 ) originates, by 1 IJ U ; and that for the orange-red band of Na 2 , by 
1 i7+. The potential curves derived from the band analysis are repro- 
duced for Na 2 in Figure 68A. 

rules governing transitions l II -*■ 1 E 

30 000 



In agreement with the 
(Section 45), the resonance 
spectra of Na 2 consist partly 
of doublets and partly of 
singlets. The resonance series 
show maxima of intensity 
at their long-wavelength and 
at their short-wavelength 
ends and a minimum of in- 
tensity in the middle. From 
every excited level v', two 
transitions have the highest 
relative probability, namely, 
those from the two turning 
points on the potential curve 
of the excited state A in 
Figure 68. The one corres- 
ponds to a relatively small, 
the other to a large value of 
hv. These experimental facts, 
combined with the F.C. prin- 
ciple in its elementary form, 
prove that the minima of the 



25000 



20 000 



15000 



10000 



5000 



^ No(3S)+ No I3P ) 




Fig. 68. potential curves of Na a (Loomis 
and Nile). 



potential curves of the excited state and the ground state {A and N in 
Figure 68) correspond almost exactly to the same internuclear 
distance r . A striking result obtained by Wood in his earliest inves- 
tigations is now easily understood : if the fluorescence was excited by 
light which was selected from a carbon arc spectrum by means of a 
monochromator and consisted of a narrow range in the blue-green, the 
fluorescence spectrum was divided into two parts : the first coincided 
very closely with the spectral range of the primary light, whereas the 
other, separated from the first by a dark interval, was situated at 
greater wavelengths. If the monochromator selecting the exciting light 
was set for greater wavelengths, the long-wavelength part of the 
fluorescence spectrum was displaced towards the violet until the two 
parts met in the middle. For the same reason, the resonance spectra 



174 DIATOMIC GASES AND VAPORS 

which are excited by strictly monochromatic radiation in the blue- 
green band system contain, in general, in addition to the nearly 
equidistant series starting from the exciting line, a great number of 
closely spaced weaker lines in the yellow-green. These belong to 
transitions to the highest vibrational levels of the ground state and 
are difficult to disentangle because of the small values of AG" (i860). 
Brown has carried through a calculation of the intensity dis- 
tribution on the basis of the wave-mechanical formulation of the F.C. 

principle for the two Na 2 resonance 
I 1 spectra excited by Cd-lines 4800 

I I 1 I 1 1 and 5086A (*, Table 31). He made 
the simplifying assumption that 
the molecules in both electronic 
[ I I I I 1 states can be represented by har- 
monic oscillators as long as the 
vibrational quanta v' and v" are 
comparatively small. The effective 
frequency o>* was assumed to be 



observed. b: calculated for 
■ 5. c: calculated for v' = 6. 



""0 2 <» 6 8 10 12 14 the mean of the fundamental 

Fig. 69. Intensity distribution in frequency ta e and the frequency of 

the Na 2 resonance spectrum excited the vibrational state v: co v = 

by Cd-line 4800A (Brown) ; {v ^ ^ _ (y + ^2^ Accor . 

ding to an older analysis, the 
quantum number v' = 6 had been 
assigned to the upper level of the singlet resonance series which is 
excited by the Cd-line 4800A. Figure 69 shows a comparison between 
the experimental measurements and Brown's calculations iovv' = 5 
and 6, respectively. From the excellent agreement between a and b 
it follows with certainly that v' = 5 is the correct evaluation* {175, 

675). 

The agreement between calculation and observation is almost 
equally good for the doublet series excited by the line 5086A which 
consists, apart from the exciting line, only of four anti-Stokes 
members (see Table 31). 

The red band system of Na 2 also forms a part of the absorption 
spectrum of the vapor and, accordingly, the spacing AG" of the re- 
sonance spectra excited in this system has the same value as in the 
resonance series of the blue-green band system. Apart from the fluo- 

* The appearance of a very weak anti-Stokes line in the resonance spectrum 
excited by the line 4800 proves that transitions 6' ■*- l" must also occur to some 
extent in the absorption process. 



FLUORESCENCE of KNa, K 2 , Li 2 , Rb 2 , AND Csa 175 

rescence produced by white light, Wood observed only the resonance 
spectra stimulated by the Li-lines 6102 and 6708A. In the absorption 
spectrum, the system stretches somewhat beyond the D-lines in the 
direction of smaller wavelengths. The corresponding transitions 
[indicated by the first arrow (from the left) in Figure 68] originate 
from high vibrational levels which are little populated at the tempera- 
tures of the experiments, and, therefore, this part of the band is weak. 
Nevertheless, irradiation of sodium saturated at300°C with the intense 
light from a sodium arc produces, in addition to the atomic D-lines as 
surface fluorescence, the emission of two molecular resonance series 
originating from the D-lines and showing many anti-Stokes members. 
Even before this had been proved conclusively, Schueler suggested 
that the appearance of a series of bands close to the D-lines in the 
spectrum of glow discharges in sodium vapor and of chemical reactions 
with sodium was due to a secondary process : primarily, sodium atoms 
are raised into the 3 2 P-states by electron impact and, in a second 
process, their energy is transferred on to Na 2 -molecules. The question 
whether this transfer occurred by collisions of the second kind, or by 
radiation, was left open. This is the first instance of the mechanism 
which Kimura later called "auto-resonance" (see Section. 49) (176, 
i4yy,igoo,igo8,igog), 

Wood observed fluorescence in the band system adjacent to the 
second member of the principal atomic series of Na (3303A) caused by 
irradiation with the nonresolved radiation from a carbon arc. Later, 
Seidel succeeded in exciting resonance series by absorption of the 
Ag-lines 3391 and 3383 A and also, of some Cu- and Zn-lines. By the 
emission of these resonance spectra, the excited molecules return to 
the ground state and, thus, the spacing AG in these progressions is 
again of the order of 150 cm" 1 (1201a, 1483, 1868). In the absorption 
spectrum of N^-vapor, the band system between 3600 and 3200A 
has been analyzed recently by Pearse and Sinha who were able to 
represent the progression of band heads with great accuracy using 
the constants listed in Table 32 although these were derived from the 
analysis of the blue-green bands (1201a). 

54. KNa, K 2 , Li 2 , Rb 2 , and Cs 2 . Our knowledge of the fluorescence 
of the diatomic molecules of the other alkali metals is much less 
complete. Apart from the fluorescence caused by white light, a few 
resonance series have been photographed in the red band system of K 2 
and in the orange system of KNa ; both are produced by a mechanism 
analogous to that responsible for the blue-green system of sodium. 
In the case of K 2 , the resonance spectra were excited by the two yellow 



176 DIATOMIC GASES AND VAPORS 

mercury lines and the two D-lines. The constants for the equations 
by which the spectra can be represented are contained in Table 32. 
Some additional molecular bands, corresponding to other electronic 
transitions, appear in the absorption spectrum of potassium vapor, but 
they have not been observed in fluorescence emission {1283, 1295, 1894) ■ 

The heat of formation of the K 2 -molecules was determined for the 
first time by using the intensity of the band fluorescence as a measure 
of the number of molecules present per unit volume and by varying 
the temperature of the vapor, either at constant pressure or at 
saturation pressure. The heat of formation was thus found to be about 
14,000 cal per mole or 0.6 eV, in very satisfactory agreement with 
later, more accurate, determinations (211). 

Fluorescence of Rb 2 and Li 2 was observed only under excitation 
with white light. Li 2 exhibits, under these conditions, a band in the 
red. According to Carter and to Dunoyer, the fluorescence spectrum of 
Rb 2 consists of three groups of bands, one in the red, one in the orange, 
and one in the green. At low temperatures the red group predominates ; 
it stretches from 6700Ainto the infrared and its numerous bands coincide 
with those of the strongest absorption band system. Probably it is ana- 
logous to the blue-green bands of Na 2 and corresponds to the transition 
1 77- 1 27. Its intensity decreases at temperatures above 300° C, as com- 
pared with the intensity of the two other band groups (213, 320,1912) . 

In the absorption spectrum of cesium vapor, five independent 
band systems were obtained by Loomis between 4800 and 9000A. A 
band with the maximum of intensity at 7667A is already very strong 
at 170° C and shows a long progression of band edges. Loomis ascribed 
it also to the transition from the ground state of the molecule 1 S to a 
state 1 IJ. While the band at 7667 could not be observed in fluorescence 
under excitation with white light, another band near 6250A appeared 
in the emission spectrum, probably only because of its more suitable 
spectral location. In the absorption spectrum this band becomes 
noticeable at 230° C; it shows an extremely complicated structure, so 
that Loomis was unable to analyze it or to assign it to a definite 
electronic transition. He succeeded, however, in exciting a resonance 
progression by means of the neon line 6402A; the series consisted of 
six "positive" lines with a spacing AG of the order of magnitude of 
40 cm -1 . Since the lower state of a band system appearing in the ab- 
sorption spectrum at such low temperatures must be the electronic 
ground state of the molecule, the constants obtained from the reso- 
nance spectrum are characteristic of the Cs 2 -molecules in the state 
^ {956,998,1375). 



FLUORESCENCE AND RESONANCE SPECTRA OF OXYGEN 1 77 

D. Elements of the Sixth Column of the Periodic System 

55. Oxygen. Next to the vapors of iodine and sodium, the fluores- 
cence and resonance spectra of diatomic molecules have been most 
extensively investigated in the vapors of the elements of the sixth 
group of the periodic system. The spectral regions in which the exci- 
tation and the emission of fluorescence occur in each of these elements 
are listed in Table 33. 

Table 33 

Approximate Location of the Absorption and Fluorescence 

Bands of 2 , S 2 , Se 2 , and Te 2 

(Wavelengths in A) 



Element 


o„ 


s 2 


Se, 


Te 2 


Absorption 
Fluorescence . . 


< 1900 
<2000-3870 


2548-4000 1 3238-4180 
2800-5650 3050-4910 


3831-6200 
4200-6600 



On account of the light absorption by atmospheric air, the first 
strong absorption band system of oxygen is accessible only to the 
methods of vacuum spectroscopy. The bands below 1900A, which are 
obtained on spectrograms if the light from a high -pressure meicury 
lamp is passed through a layer of atmospheric air before falling on the 
slit of a spectrograph, were interpreted erroneously by Steubing as 
produced by fluorescence of oxygen; they are, in reality, oxygen ab- 
sorption bands visible on the continuous background of the lamp 
spectrum. However, Rasetti obtained a series of resonance doublets by 
irradiating pure oxygen of atmospheric pressure with the mercury line 
1849A, which coincides with one of the last bands of the 2 band 
system. The series was photographed from the eighth positive member 
at 2364A to the twenty-second member at 3870A. According to the 
very complete analysis of the 2 band system under consideration 
(the so-called Schumann-Runge bands) the excited state of this 
resonance series is v' = 8, J' = 12, whereas the ground state from 
which the excitation takes place corresponds to v" = (1341,1573). 

A rather intense fluorescence was observed in oxygen at low 
pressure (0.5 mm) by R. W. Wood and others when they irradiated the 
gas with short-wavelength u.v. originating from various spark dis- 
charges. No attempt has been made to analyze this spectrum (1000, 
1022, 1164,1880, 1905) . 

56. Resonance Spectra of S 2 , Se 2 , and Tej. According to Steubing, 
Pringsheim 7 



178 



DIATOMIC GASES AND VAPORS 



the vapors of sulfur, selenium, and tellurium can be excited to fluo- 
rescence by the unresolved radiation from iron or carbon arcs and 
from various spark discharges. The fluorescence spectra consist of 
channeled bands which continue absorption band systems of a similar 
structure towards greater wavelengths and overlap them to a certain 
extent. Later investigations by Rosen and others showed that these 
fluorescence spectra produced by "white light" are also essentially an 
inversion of the absorption spectra, although stretching farther into 
the region of greater wavelengths (Table 33) {1001,1378,1379,1575). 

Under excitation with monochromatic light, doublet progressions 
again appear, instead of the complete band systems. In contra- 
distinction to iodine vapor, the vapors of sulfur, selenium, and tellurium 
contain not only diatomic but also polyatomic molecules in equilib- 
rium according to temperature and pressure. Since the band spectra 
which are here under consideration belong only to the diatomic 
molecules, their intensity depends essentially on the choice of those 
two parameters. In order to vary them independently, the temperature 
in the observation chamber and in a side tube containing the solid 
material must be regulated separately. Table 34 shows the relation be- 
tween the intensity of the band fluorescence and the temperature at a 
constant vapor pressure of 10 -1 mm for the three elements. 

If, on the other hand, the temperature is kept constant at about 
500° C, the fluorescence intensity begins' to become appreciable at a 
pressure of 10~ 3 mm and thence increases nearly proportionally with 
density. At pressures > 1 mm, the fluorescent region contracts itself 
to the neigborhood of the entrance window for the primary radiation 
and remains observable as "surface fluorescence" up to rather high 
pressures — at least up to 250 mm in sulfur, to 50 mm in selenium, 
and to 30 mm in tellurium vapor. Since the various exciting lines are 



Table 34 

Fluorescence Intensity of the Vapors of Sulfur, Selenium, 
and Tellurium 





(Pressure 10 


1 mm) 




Element 


Sulfur 


Selenium 


Tellurium 


Just noticeable at . 


150° 


350° 


400° 


Increases up to 


400° 


600° 


800° 


Constant up to 


600° 


800° 


— 


Decreases above . . 


650° 


— 


— 



RESONANCE SPECTRA OF Sjj, Se 2 , AND Te 2 1 79 

absorbed to very different degrees in the vapors, according to whether 
the absorption process originates from vibrational level i " = 0, 1 , 2 . . . , 
the state of surface fluorescence occurs for various progressions at 
widely different pressures. In tellurium vapor, for instance, the 
mercury line 5461 A only begins to excite a faint "beam fluorescence" 
at a pressure of 10 mm, while a resonance series excited by the line 
4358A appears exclusively as surface fluorescence under these 
conditions. 

The absorption band systems of Table 33 correspond to transi- 
tions 1 Z- 1 I] for all three of the elements and, therefore, the resonance 
spectra should consist of doublet series. However, this could' be 
demonstrated only in very few cases. Generally, exceedingly com- 
plicated line groups were obtained instead of the expected doublets, 
because the exciting lines covered several absorption lines. This is 
caused, at least partially, by the existence of several isotopes of the 
elements which combine to a number of molecules with slightly 
different spectra (768, 1605,1607,161?, 1732). 

In several resonance spectra of tellurium vapor, the individual 
components of such line groups or apparent multiplets could be 
assigned to various combinations of the tellurium isotopes with the 
atomic masses 124, 125, 126, 128, and 130. According to Rosen, a 
very intense resonance spectrum excited in tellurium vapor by the 
mercury line 4358A can be followed up to the group at 6530A which 
corresponds to v" = 36. Since the exciting line lies close to the head 
of the band 8'-4", the isotope effect is not strong enough in the first 
members of the series (corresponding to low v"-values) to split them 
into distinct components; the apparently single lines are only 
broadened and made diffuse. However, for v" greater than 22, each 
member consists of five well separated lines, and their separation 
increases with increasing values of v". The number of the observed 
components is smaller than 15 (the number of possible combinations 
of the five isotopes) not only because of the very small concentration 
of some of the isotopes, but also because the lines belonging to com- 
binations with nearly equal reduced masses (like 128 + 128 and 
130 + 126, or 126 + 128 and 124 + 130) coincide almost exactly {1383). 

For sulfur vapor, the evidence for the existence of the isotope 
effect is less complete; however, Swings made the assumption at least 
very plausible that not only molecules made up from the most 
frequent isotope S 32 contribute to the emission of some of the resonance 
spectra, but that also molecules containing an atom of the odd isotope 
S 33 take part in the process. 



180 



DIATOMIC GASES AND VAPORS 



[In every electronic state of an element molecule consisting only 
of atoms without nuclear spin (even atoms), even or odd rotational 
quantum numbers should occur exclusively (see Section 45) ; according 
to Swings' analysis, some resonance spectra of sulfur vapor — for 
instance, the spectrum excited by Hg 2967A — exhibit groups of 
doublets with rotational quantum numbers which are partially even 
and partially odd. Analogous considerations were applied by Swings 
to resonance spectra of Te 2 and Se 2 , with the conclusion that various 
isotope combinations are present also in these vapors (i6og,i6i4). 

The numerous resonance spectra which were observed in the 
vapors of sulfur, selenium, and tellurium are collected in Table 35 
{343,438,472,477-481,534,879,1195,1237,1238,1325,1374,1604). 

The spectra are represented satisfactorily by the following 
equations : 

S 2 : v = v — 724.5w" + 2.91i/' 2 (53) 

Se 2 : v = v — 397.5v" + 1.32k" 2 
Te 2 : v = v a — 250.4f " + 0.53u" 2 

In the fluorescence spectrum of selenium, a second band system 
has been observed in the region of shorter wavelengths. According to 



Table 35 
Resonance Series in the Vapors of S 2 
(A = exciting line in A; N~ = number of observed anti-Stokes members) 



Se 2 , and Te 2 



Se 


Se 2 


Te 2 


h 


v" 


N~ 


h 


v" 


v' 


N- 


h 


v" 


v' 


N- 


Hg 2894 





1 


Hg 3650 


6 


10 


4 


Hg4067 


3 


19 


2 


Ag 2897 


4 





Hg 3655 


3 


4 


3 


Pb 4058 


5 


23 


3 


Ag 2929 








Mg3829 


— 


— 


2 


Hg 4078 


2 


16 





Ag 2934 








Mg 3832 


— 


— 


2 


Cu 4036 


2 


16 


2 


Mg 2937 


— 


1 


Mg 3838 


— 


— 


2 


Pb 4245 


10 


24 


3 


Hg2968 


2 


1 


Ba 3892 


6 


3 





Hg 4358 


4 


8 


4 


Hg 3022 


— 


4 


Ca 3934 


8 


5 





Cd 4416 


8 


13 


9 


Hg3126 


5- 


3 


Ca 3969 


8 


4 





Mg 4481 


5 


6 


5 


Hg3131 


5 


3 


Cu 4024 


•7 


1 


5 


Cd 4678 


8 


13 


8 


Cu 3248 


5 


3 


Hg4047 


7 





4 


Zn 4723 


8 


3 


4 


Cu 3274 


5 


3 


Cu 4063 


7 





6 


Cd 4800 


12 


7 


5 


Ag 3281 


2 


2 


Hg 4078 


7 





3 


N 5005 


13 


3 


3 


Cu 3287 


4 


3 


Hg 4358 


13 


3 


10 


Hg5461 


17 





4 


Cu 3308 


5 


3 


Ba 4525 


16 


4 


3 










Hg 3502 


12? 





Ba 4554 


16 


3 


6 










Hg,3655 


7 


2 



















PREDISSOCIATION AND FLUCTUATIONS 



181 



Diestelmeiei , a group of emission bands is obtained by irradiating the 
vapor with the light from an iron spark. The fluorescence was sup- 
pressed by inserting a plate of glass into the path of the exciting light. 
Probably the same bands formed a part of the fluorescence spectrum 
reaching from 2229A to the limits of the visible region which was 
excited by McLennan and Wallerstein in selenium vapor saturated at 
325° C by the unresolved radiation from a mercury arc (305,1001). 

57. Predissociation and Fluctuations. In the band systems of S 2 , 
Se 2 , and Te 2 , a phenomenon occurs which was discovered by V. Henri 




3.6 V V,+ 'o 

2.8V 'Pt+'Po,, 

2.3 V *>,+"/», 



Fig. 70. Potential curves of Te 2 (Rosen). 
Shaded area : region of fluctuation bands. 

and was called by him "predissociation." In the neighborhood of a 
certain vibrational state with v' = v' p , the absorption bands become 
diffuse and the fine structure due to the rotation disappears. The 
phenomenon is explained by assuming that the potential curve of the 
excited state is crossed at the point v' p by the potential curve of another 
electronic state, or at least that the two curves approach each other 
very closely. The potential curve of the "perturbing state" is frequent- 
ly a pure repulsion curve (C in Figure 70) or an attraction curve with 
a very shallow trough (C and C" in Figure 70), corresponding to a 
loosely bound unstable molecule. The perturbing curve causing the 
predissociation may even have a deep minimum corresponding to a 
stable molecular state, if the point of intersection lies higher than the 
dissociation level of this state. The mechanism is very similar to that 
represented by Figure 48 for the quenching of an excited atom by a 
collision of the second kind. 

If a spontaneous radiationless transition from curve A to curve 
C in Figure 70 is allowed, the lifetime of the excited state A becomes 
shorter and the absorption lines due to the transitions A <- N are 



1 82 DIATOMIC GASES AND VAPORS 

broadened so that they overlap and render the band diffuse. In the 
emission spectrum, the corresponding lines are almost completely 
missing because the effect becomes noticeable only if a spontaneous 
transition from A to C has a much higher probability than the tran- 
sition from A to N. 

In the band system of tellurium, for instance, predissociation 
causes the bands to become diffuse in the neighborhood of wavelength 
3895A; no resonance spectra can be excited by lines belonging to 
transitions with w'>20 and, in the complete fluorescence band 
system excited by white light, all bands which originate from vi- 
brational levels with v' > 21 are absent. 

The fluorescence band systems of Se 2 and Te 2 (Table 33) are 
continued at their long-wavelength end by a sequence of more or less 
diffuse bands. These bands are also observed in the spectra excited by 
electric discharges and in thermal radiation ; at high temperatures they 
appear even in the absorption spectra of the vapors. Evidently the 
emission process transfers the molecules into the higher vibrational 
levels of the electronic ground state. Since the bands are emitted at 
lower temperatures by thermal radiation than the bands listed in 
Table 33, the excited level from which they originate must be lower 
than the excited state for the latter bands. According to Rosen and his 
collaborators the new excited states are represented by shallow po- 
tential curves C" and C in Figure 70. Spontaneous transitions from A 
into C" and C* must be allowed. The existence of two curves of this 
type is assumed because the bands seem to be divided into two groups 
each. Table 36 contains, under AG, the spacing of the principal 
maxima, and under Av, the distances between secondary maxima 
superimposed upon most of the bands. These secondary maxima are 
apparently caused by the fact that the curves C" and C" belong to 
weakly bound molecular states with closely spaced, but still quantized, 
vibrational levels. Spectrographs of small dispersion do not resolve 
these secondary maxima, so that the bands appear to be mere fluctu- 
ation bands. Bands of this type, with a "fluctuating intensity distri- 
bution", may be called pseudofluctuation bands. From the values of 
AG in the C'-bands of Te 2 , values of v" between 12 and 15 are derived; 
v"s between 15 and 20 are obtained for the C-bands of Te 2 ; and, for 
the bands of Se 2 , v" is also larger than 12 {1033,1380-1382). 

The processes here under consideration differ from predissociation 
processes in that the states characterized by the curves C and C" 
must have a lifetime sufficient for the emission of fluorescence and that, 
furthermore, the probability of the transition from ^ to C or C", 



PREDISSOCIATION AND FLUCTUATIONS 



183 



and from there to N, must not be large compared with the probability 
of a spontaneous transition from A to N. It must be kept in mind that 
if the transition from 4 to C or C* is possible, the molecules are also 
able to return from C or C" to A. Thus, this transition probability is 
not essentially responsible for the relative intensities of the normal 
resonance fluorescence and the pseudofiuctuation bands. If the fluo- 
rescence of Se 2 or Te 2 is excited by suitable lines — for instance, the 
Mg-triplet 3829, 3832, 3836A which is effective in both vapors — the 
typical resonance series and the pseudofiuctuation bands are emitted 
with comparable intensities. 

Table 36 
pseudofluctuation bands of se 2 and te 2 



Element 


Te, 


Se a 




C 


C" 


a 


C» 


Wavelength (A) 


5250-6015 


6022-6359 


4770-5160 


5380-6080 


Number of 










fluctuations . 


— 


— 


5 


8 


A Gin cm -1 . . 


250 


220 


360 


330 


A v in cm -1 


20 


20 


30 


45 



The intensity of the pseudofiuctuation bands is practically 
independent of the temperature and the gas pressure ; these parameters 
would have a strong influence if the transitions from A to C and C" 
were caused by collisions of the second kind. On the other hand, 
"radiating transitions" from A to C (and C") are out of the question 
because of the selection rules forbidding radiating transitions between 
two states from which radiating transitions to a common third state 
(the ground state) are possible. Thus, the transitions from A to C and 
C" must be spontaneous and direct. 

The pseudofiuctuation bands of selenium were also obtained by 
irradiating the vapor with white light of wavelengths 3600 to 4200A. 
The spectrum had essentially the same appearance as when excited 
by monochromatic light, but every fluctuation group contained more 
secondary maxima ; the same is the case if the emission of the bands 
is caused by electrical or thermal excitation. Apparently the distri- 
bution over the closely spaced vibrational levels of the states C and C" 
depends on the vibrational quantum number v' of the state A from 
which the molecules reach the states C" or C. As mentioned in 



184 DIATOMIC GASES AND VAPORS 

Section 50, the Mc bands of iodine show a similar behavior. It is not 
improbable that the short -wavelength bands designated in Section 50 
as fluctuations have also a secondary structure which is covered by 
the superimposed "maze of lines" and that they belong, therefore, to 
the class of pseudofluctuation bands dealt with here. 

E. Fluorescence of Other Diatomic Molecules 

58. Elements of the Fifth Column of the Periodic System. The fluo- 
rescence of other diatomic molecules has been observed occasionally, 
but the data are not sufficient, in general, for the determination of the 
terms between which the corresponding transitions take place. 

The first strong absorption band system of N 2 lies still farther in 
the u.v. than that of oxygen and has never been obtained in fluo- 
rescence. However, Oldenberg observed a number of bands between 
3700 and 4700A by exciting nitrogen at 0.5 mm with light of short 
wavelength (probably less than 1500A) from a spark. The fluorescence 
spectrum consisted not of resonance progressions originating from a 
definite upper vibrational level, but of complete bands corresponding 
to transitions between two higher electronic states of the N 2 -molecule 
which are known also from other spectroscopic investigations. By the 
irradiation of atmospheric air with the light from a powerful spark 
between aluminum or copper electrodes, Wood and Meyer obtained 
the emission of the nitrogen bands at 3369, 3536, and 3778A; the last 
occurred with much higher intensity in pure nitrogen (in the absence of 
oxygen) (1000,1021,1022,1163,1164) . 

The principal results obtained with the other elements of this 
group are collected in Table 37. The figures in the last line of the table, 
which are marked with an asterisk, represent the fundamental 
vibrational frequencies ox e derived from the observed values of AG; 
in the other spectra, the available measurements do not suffice for the 
determination of this constant. Two widely different values of AG were 
found by Parys for the resonance series excited in Bi 2 -vapor by the 
blue and the green mercury lines ; either the two progressions corre- 
spond to transitions to different lower electronic states, or the green 
fluorescence transfer the molecules into very high vibrational levels 
of the electronic ground state [v" > 50). The series excited by the blue 
line has no anti-Stokes member and seems to consist of triplets which, 
however, are probably due to the superposition of two doublet series 
with Sv = + 16 and — 20 cm -1 , respectively. The green doublet 



FLUORESCENCE OF VARIOUS METAL VAPORS 



185 



series, with Sv= 12 cm -1 , has live anti-Stokes, and five positive 
members. Parys described several additional fluorescence bands ex- 
cited in bismuth vapor by the green mercury line, but could not 
assign them to any known electronic transitions. While at lower 
temperatures and pressures only the atomic fluorescence lines are ob- 
served (cf. Section 15), the blue resonance series appears in the fluo- 
rescence spectra of the saturated vapor at 500° C and the green series 
above 800° C. By irradiation of Bi-vapor with white light at 1300° C, 
Narrajan and Row obtained twenty-four fluorescence bands between 
5000 and 6600A which coincided with the absorption bands found by 
the same investigators {iog6,ng2, 1338,1610). 

Table 37 

Fluorescence of the Elements of the Fifth Group 

of the Periodic System 





P a (678,685) 


As 2 {1618) 


Sb, 


Bi 2 


Temperature 
in ° C 


600-700 


1100 


900 


500-1300 


Vapor pressure 


0.1 mm 


saturated 
at 300° C 


saturated 
at 600° C 


saturated 


Fluorescence 
spectrum 
in A 


1900-3500 






5000-6600 


Exciting . . 
lines for . 
resonance 
series in A 


Al 1935, 1990 
Cd2144, 2195 
Zn 2026, 2064 
Zn2101 


Hg 2483 
Hg2537 
Hg2655 
Hg 2806 


Hg 2968, 3022 
Hg3126, 3132 
Mg2929, 2937 


Hg 4358 
Hg 5461 


A G in cm -1 . . . 


770* 


420 


277*f 


309; 173.2 



f According to Genard; for Sb 2 Siksma gives m e = 269.5 

Similarly, the atomic resonance lines alone are excited in Sb 2 - 
vapor saturated at 200° and superheated to 900° C. Only if the oven 
regulating the vapor pressure is heated to 600° do the molecular 
resonance series of Table 37 appear in the fluorescence spectrum {483). 
At somewhat lower pressures, Siksma observed the emission of some 
bands excited in antimony vapor by the light from Mg and Zn sparks; 
there are no data available concerning the origin and the structure of 
these fluorescence bands (1503). 

59. Various Metal Vapors. — The vapor of lead has been investigated 
by Domaniewska-Krueger and Klokowska. By irradiation with white 



1 86 DIATOMIC GASES AND VAPORS 

light at 900° C, they obtained the emission of a band system stretching 
from 3200 to 5136A in which 23 edges could be distinguished 
between 4216A and the long wavelength end of the system. Resonance 
series were excited by the mercury lines 3287, 3345, 4358, and 5461 A. 
In the two latter spectra, the individual members could be resolved 
into doublets with 8 v = 35 and 24.4 cm -1 , respectively. For the u.v. 
series, the spacing AG is of the order of 430 cm -1 , corresponding 
probably to the approximate value of a>" e ; for the series in the visible, 
AG is only about 420 cm -1 . The authors give equations with a member 
quadratic in v" for their resonance spectra; however, since their 
values of o> e x e vary between 0.7 and 2.07 for the various series, the 
measuring accuracy does not seem to have been sufficient for this 
calculation (3og,y88). 

The vapors of thallium and indium exhibit a number of absorption 
bands at higher vapor pressures. These probably belong to diatomic 
molecules Tl 2 and In 2 . Absorption in these bands, however, leads only 
to the emission of atomic lines, according to a mechanism which is 
treated in a later section. The molecular bands themselves could never 
be obtained in the fluorescence spectra (1783). 

60. Light and Heavy Hydrogen. The first absorption bands of 
molecular hydrogen are situated in the far u.v., in the neighborhood of, 
and below, 1060A. They correspond to the transition of molecules from 
ground state lsa 1 i7+, to various electronic states A, B, C. In the 
emission spectrum of an electric discharge through argon with a small 
admixture of hydrogen, Beutler observed a doublet series consisting of 
fourteen members in addition to the normal Lyman bands {A -> N) 
which are excited by collision processes. The spacing AG of the series 
and the doublet separation Sv can be derived from the well-known 
constants of the ground state of H 2 , if it assumed that the v"s progress 
from 1 to 14, while the rotational quantum numbers are K" = 1 and 3, 
respectively, corresponding to the value K' = 1 for the excited state. 
According to Beutler, this series is produced by the absorption of the 
argon line 1066A, which occurs with great intensity in the spectrum 
of the discharge and which transfers the hydrogen molecules from the 
ground state V = 2, k" = 1 to the level v' = 10, K ' = 2 of the 
electronic state B (2piT l n u ). The calculated energy of this transition 
agrees with the h v of the argon line within 2 cm -1 . The energy of the 
vibrational level v" = 2 of the ground state is 8085 cm -1 or 2300 cal 
per mole; it is so high that the equilibrium concentration of the 
molecules in that level is only 10 -8 and their partial pressure is not 
more than 10~ 10 mm at the temperature and the hydrogen pressure 



FLUORESCENCE OF METAL HALIDE VAPORS 187 

in the discharge tube. This is far too little to provide sufficient ab- 
sorption of the argon line; it must, therefore, be assumed that an 
adequate number of molecules in this state is produced by the dis- 
charge itself. 

Similar resonance spectra originating from HD-molecules were 
obtained under the same conditions of excitation in mixtures of light 
and heavy hydrogen. In this case, the molecules are raised from the 
nonvibrating level of the ground state to the level v' = 3 of the 
electronic state A ; thus, the series forms a part of the band system 
analogous to the Lyman bands of norma] hydrogen. The spectrum 
consists of twelve doublets without an anti-Stokes member; from the 
spacing AG, which decreases along the progression from 448 to 202 
cm -1 , the rotational quantum number K' = 2 (K" — 1 and 2) can be 
derived. A weaker companion line of these doublets is ascribed to 
a second series belonging to the same bands, with K' = 1 (104,1026). 

In the HD resonance spectrum, the doublets with v" = 3, 6, 
and 9 have vanishingly low intensities, while those with v" = 5 and 
8 are the strongest. The theoretical intensity distribution could be 
derived from quantum mechanics and was found to be in good 
agreement with the experiments. A better approximation could be 
applied by Bewerndorff in the determination of the eigenfunctions of 
the vibrating hydrogen molecules than had been used by Brown for 
the resonance spectra of Na 2 (compare Section 53). 

Apart from these Lyman band series, four doublets between 1050 
and 1200A were found in the emission spectrum of HD. They originate 
from the argon line 1048 A and are related to another band system (the 
so-called Werner bands). The only vibrational level of theground state 
in which the line 1048A can be absorbed in v" = 1, with K" = 2. Since 
the relative intensity of this series increases appreciably with increasing 
temperature, it must be assumed that its appearance is favored by 
the thermal increase of the number of HD-molecules with v" = 1 . 

Heavy hydrogen, D 2 , does not exhibit a phenomenon of this type ; 
no electronic transitions which are in resonance with one of the argon 
lines exist in D 2 . 

61. Metal Halide Vapors. The vapors of several metal halides 
provide practically the only examples of polar diatomic molecules 
which are known at present to be fluorescent.* AgCl, AgBr, Agl, and 

* Terenin occasionally mentioned the emission of a fluorescence band 
between 5800 and 2400A which is excited in CO by light of wavelengths below 
1600A. According to a casual remark of Sen Gupta, the so-called y-bands of 
NO can be produced by irradiating nitric oxide with light of wavelengths 
somewhat greater than 2000A. (See also the following section). 



188 



DIATOMIC GASES AND VAPORS 



Til have so far been investigated. The absorption spectra of these 
vapors consist, in part, of bands showing a fine structure and corre- 
sponding to transitions from the ground states of the molecules to 
excited states with discrete vibrational levels. Typical resonance 
spectra can be produced by light absofption in these bands. The ap- 
proximate spectral location of the bands and the vibrational fre- 
quencies of the electronic ground states obtained from the resonance 
spectra are collected in Table 38. The table contains, furthermore, the 
heat of dissociation D" of the normal molecules and, in the last row, 
the "Reststrahlen" frequencies of the compounds. The latter vary in 
the same order as the a>Js, but their absolute values are much smaller, 
indicating that the atoms are less strongly bound in the ionic crystal 
lattices than in the molecules of the vapor. T and p are the tempera- 
tures and pressures under which resonance spectra have been obtained, 
N~ and N + the numbers of anti-Stokes and positive members contained 
in the resonance series which were excited by various primary lines 
(422). 

Table 38 
Resonance Spectra of Metal Halides 



Compound 


Agl 


AgBr 


AgCl 


Til 


Absorption 
bands (A) 


3168-3350 


3183-3394 


3116-3485 


3780-5360 


T(°C) 
p (mm) 


800 
0.5 


900 
1.5 


— 


500 
6 


Exciting 
lines (A) 

N- 
N+ 


Cu 2374, Ag 3383 

4 — 

35 — 


Cd 3261 
3 

8 


Zn 3175 
1 
3 


Pb 4062, Hg 4047 


<o" e (cm -1 ) 
D" (eV) 
v, (cm -1 ) 


205 
3.1 


245 
2.6 
88.9 


340 

2.1 
122.7 


150 



By irradiation with the unresolved light from an iron arc, a blue 
band fluorescence is excited in Til-vapor. By using for excitation the 
cyanogen bands emitted by a carbon arc, the structure of the very 
complicated band system becomes considerably simpler, so that the 
bands can be resolved into series with the two periods AG X = 150 and 
AG 2 = 30 cm -1 . The first one occurs also in the resonance spectra 
excited by monochromatic light and corresponds to the vibrational 



FLUORESCENCE OF DIATOMIC RADICALS 189 

frequency of the ground state ; the other period of about 30 cm -1 can 
be caused only by the vibrational frequency of the excited electronic 
state and, in this "respect, Til differs widely from the silver halides. 
According to Franck and his collaborators, the bond between the two 
nuclei, in the case of the silver halides, is of nearly the same strength 
in the ground state and in the first excited state. On the other hand, 
Butkow found that the first excited state of thallium chloride must be 
represented by a very shallow potential curve in order to explain the 
structure of the absorption spectrum of the vapor. A weak fluorescence 
excited in TICl-vapor consisted of a sequence of narrows bands be- 
tween 3200 and 3350A which seemed to coincide with some of Butkow's 
absorption bands. In such cases, where the molecules are loosely bound 
in the excited state, the discontinuous part of the band system in 
which resonance radiation can be excited is relatively narrow, and 
transitions into the nonquantized region have a great probability. In 
the case of the alkali halides, the potential curves of all excited states 
are so shallow that light absorption always leads to the dissociation 
of the molecule (see Section 70) {igi). 

The fluorescence of Til-vapor can also be excited by light of 
wavelengths below 2100A, but the intensity distribution within the 
bands is quite different. It has been suggested that this fluorescence, 
and also the occurrence of some additional continuous bands excited 
by short-wave u.v. is due to a primary process in which the dissocia- 
tion of a molecule is involved. [See Sections 74 and 78 (j6j7)]. 

If the vapors of cuprous iodide and cuprous chloride are irradiated 
at temperatures between 400 and 500° C with the light from sparks 
between aluminum, zinc, or cadmium electrodes, a weak visible band 
fluorescence is observed, green (about 4800-5000A) in the case of 
Cul, blue-violet (4300-4550A) in the case of CuCl. Since the frequency 
of the exciting light differs so widely from the frequency of the fluo- 
rescence and the emission spectrum is independent of the exact wave- 
length of the primary light, this fluorescence is not resonance radiation. 
Most likely the primary process is the dissociation of Cu 2 CI 2 or of 
Cu 2 I 2 , which are also present in the vapors, into an excited and an 
unexcited diatomic molecule. This mechanism is treated, together 
with other similar phenomena, in Section 94 {i64g). 

62. Fluorescence of Diatomic Radicals. The fluorescence of various 
diatomic radicals can be excited by the collision of polyatomic mole- 
cules such as H 2 or NH 3 with excited mercury atoms, or by the dis- 
sociation of the molecules caused by the absorption of short-wave u.v. 
light. Under these conditions, the fluorescence of the radicals OH, NH, 



190 



DIATOMIC GASES AND VAPORS 



and CN has been observed, and, moreover, the fluorescence of the 
diatomic molecules of the halides of mercury, cadmium, zinc, and 
lead. (See Sections 67, 74, and 94.) In these cases of indirect excitation, 
more or less complete bands appear in the emission spectra, although 
frequently with an anomalous intensity distribution. 

The spectra of comet tails contain lines belonging to bands of the 
following radicals and ions: OH, CH, NH, CN, C 2 ,CO + ,CH+,andN 2 + 
{1613,161 5, i6ig). They owe their existence to the photodissociation of 
some polyatomic molecules by the short-wave radiation of the sun, 
but it seems certain that the emission of their characteristic bands is a 
primary fluorescence process caused by light absorption in the radicals 
themselves, which are relatively long lived because of the low gas 
pressure in the comets' atmosphere. Although the spectrum of the 
exciting sunlight is continuous, many of the emission spectra have 
almost the character of resonance series produced by the absorption 
of monochromatic radiation : they exhibit only a few rotational lines 
of each band. This is true mainly for those radicals which, because of 
their polar nature, are able to lose their rotational and vibrational 
energy by infrared radiation, so that they are in the very lowest 
energy levels when they absorb a fraction of the impinging sunlight. 
By every absorption process, the rotational quantum number can 
be increased only by unity. The most important examples of this type 
are the OH-bands between 3078 and 3211 A corresponding to the 
vibrational transitions 0' -> 0", 1 ' -» 1 ", and 2' -> 2", and the NH-bands 
between 3350 and 3372A corresponding to 0'^0" and I'-* 1"; less 
prominent, but fairly well identified, are the bands of CH+ between 
3972 and 4231A and those of NH+ between 4039 and 4051A. In all 
these bands, the rotational quantum numbers of the excited states are 
K' < 2.* If, on the other hand, a C 2 -radical has acquired a high 
rotational energy, either in the primary dissociation process by which 
it is produced or by successive stepwise processes of light absorption, 
it remains indefinitely in this state. Accordingly, the intensity dis- 
tribution of the rotational lines in the "Swan bands" of the comet- 
tail spectra corresponds to a temperature of about 3000°. 

The CN-bands take an intermediate position, the rotational 
quantum numbers being in part as high as 25. However, the intensity 
distribution among the rotational lines differs widely from a normal 
temperature distribution: it shows two distinct maxima at about 
K' = 3 and K' = 9, the first corresponding to a temperature of 50° K 

* In some of the OH-bands, weak lines with K' = 3 have been identified; 
in the bands of CH, K' even reaches 6. 



VARIOUS EFFECTS PRODUCED BY COLLISIONS 191 

and the other to 400° K. Various explanations have been proposed for 
this phenomenon, but none of them is quite satisfactory. The solar 
spectrum is not uniformly continuous but is interrupted by many dark 
Fraunhofer lines which cause deep intensity minima in the spectrum. 
If such minima coincide with specific lines of the absorbing molecules, 
the corresponding doublets are missing from the fluorescence spectrum. 
This effect must be taken into account for an interpretation of the 
intensity distribution in all comet-tail bands due to fluorescence ex- 
citation by the solar radiation. However, it is pot sufficient for ex- 
plaining the anomalous intensity distribution in the CN-bands which 
occurs equally in the violet sequence, Av = — 1 (4215-3572A), and 
in the ultraviolet sequences, Av = (3883-3852A) and Av = + 1 
(3584-3572). It seems, therefore, more likely that the double maxima 
in the "rotational temperature" distribution of the CN-radicals occur 
either because the radicals originate from two different parent mole- 
cules, or because one type of parent molecules is photodissociated in 
two different ways. The last hypothesis may find some support in the 
results obtained in laboratory experiments on the photodissociation of 
C 2 N 2 and ICN-molecules (compare Sections 67 and 94). 

F. Effect of Collisions and of Magnetic Fields on the 
Resonance Spectra of Diatomic Molecules 

63. Various Effects Produced by Collisions. If excited diatomic 
molecules collide with other molecules, the same effects can be expected 
which are produced by collisions in fluorescent monatomic vapors: 
the excited system can be transferred to a closely adjacent quantum 
state, losing only a small fraction of its energy, or it can be genuinely 
quenched and lose its excitation energy almost completely. However, 
in a diatomic molecule either of these effects can be produced not only 
by the same mechanism as in an isolated atom, but also by another 
process which is actually, in either case, the more important and the 
more common one. The molecule can not only be transferred into a 
neighboring electronic state but also into another rotational or vi- 
brational level of the same electronic state; and, in addition to the 
quenching processes treated in Chapter I, the molecule can pass from 
the potential curve characteristic of the stable molecule into a 
repulsion curve intersecting it. If a transition of this type is allowed, 
it leads to spontaneous predissociation (see Section 57). If it is forbid- 
den by one of the selection rules, it can be induced by a collision; 



192 DIATOMIC GASES AND VAPORS 

following this transition, the two atoms forming the molecule separate 
and the excitation energy is transformed into kinetic energy of the 
atoms {592). 

There is no sharp boundary between spontaneous and induced 
predissociation. There are cases like that of the visible band system of 
iodine in which transitions from the excited electronic state to a 
repulsion curve do not occur spontaneously and are not even induced 
by collisions with helium atoms, whereas the somewhat stronger 
atomic fields of the heavier rare gases are sufficient for enforcing the 
transition. In the other limiting case, the spontaneous transition to 
the perturbing potential curve has a greater probability than the 
emission of radiation causing the return to the ground state — as, for 
instance, in the predissociation bands of tellurium. However, there are 
intermediate cases in which spontaneous predissociation has a relative- 
ly small probability and the effect is greatly enhanced by external 
perturbations. Under these conditions, even collisions with he'ium 
atoms can become effective. 

If collisions cause "transfers" as well as "induced predissociation" 
in a band system, the bands in the long-wavelength region of the 
system, which are due to transitions from the lower vibrational levels 
of the excited electronic state, are not only relatively less quenched 
than the others but may even be enhanced. Moreover, under these 
conditions the total quenching averaged over the whole band system 
does not obey the Stern- Volmer equation, because the quenching 
efficiency is not constant. It is larger for those molecules the vibrational 
levels of which are close to the point where predissociation occurs ; it 
becomes smaller when more of the excited molecules are transferred by 
collisions into lower levels. 

The effective cross section of a perturbing gas in its interaction 
with an excited molecule containing vibrational energy depends on 
two main factors. The first is the mass of the particles, because of the 
conversation of momentum as well as' because of the influence of mass 
on the velocity of the molecules and on the duration of the individual 
collisions ; the second is the strength of external molecular fields, by 
which the potential curves of the excited molecules are more or less 
distorted during the collisions. 

64. "Transferring Collisions" in Iodine Vapor. If molecules are 
raised by the absorption of monochromatic light into the level v'J' of 
an excited electronic state, and if they are transferred by collisions 
into other rotational levels, the singlets or doublets of the corresponding 
resonance spectrum give way to more or less complete bands ; if the 



TRANSFERRING COLLISIONS IN IODINE VAPOR 



193 




vibrational quantum number v' is also affected by the collision process, 
new bands appear in the fluorescence spectrum until finally the whole 
band system is emitted. This phenomenon was first observed by 
Franck and Wood in the resonance spectrum of I 2 -vapor excited by 
the green mercury line. Bands were already noticeable in the intervals 
between the resonance doublets when 2 mm of helium were added to 
the iodine vapor; with increasing helium pressure, they became 
stronger and more numerous. At a helium pressure of 10 mm the 
members of the original resonance series no longer stood out from the 
background formed by the other band lines, which were now also 
extended much further into 
the red region of the spectrum 
(Figure 71). This intensity 
shift in direction of greater 
wavelengths which is best 
observed if the fluorescence 
is excited by white light is 
caused by the fact that high 
vibartional energy is par- 
tially transferred from the 
excited I 2 -molecules to He- 
atoms, while the inverse pro- 
cess has a much smaller pro- 
bability. However, the major 

part of the excitation energy, which is stored in the excited electron, 
is not affected by the collisions, so that the total intensity of the 
fluorescence is not greatly altered. At a helium pressure of 20 mm the 
luminous intensity doe.3 not seem to have noticeably decreased, as 
far as the change of color makes the comparison possible, and even 
at 80 mm the fluorescence is still strong, although the color has now 
changed to red; under these conditions, every excited I 2 -molecule 
undergoes, on the average, thirty collisions during its lifetime (412, 
1872, i8gg). 

The admixture of other foreign gases or an increase of the iodine 
vapor pressure itself produces similar results, but simultaneously the 
total fluorescence intensity -is weakened to a much greater extent, the 
■degree of quenching depending on the nature of the perturbing gas. 
With argon, the red shift in the intensity distribution is still plainly 
visible; with oxygen, it is practically suppressed by the much stronger 
quenching action (Fig. 72) (430,1871) 

A change of v' and of/' of the excited molecules is produced with 
Pringsheim 7* 



Fig. 71. Transformation of a resonance 

spectrum of I 2 to the complete band 

spectrum (Franck and Wood). 

1 : pure I 2 -vapor. 2 : 2 mm He. 
3 : 10 mm He. 



194 DIATOMIC GASES AND VAPORS 

about equal probability by a collision process; the appearance of a 
new line in the same band or in a neighboring band occurs with about 
the same intensity. The "transferring yield" in collisions of excited 
I 2 -molecules with rare-gas atoms is so high that the effective cross 
sections, which increase with increasing atomic weight of the rare gas, 
are in some cases twenty-five times larger than the gas-kinetic cross 
sections (J25,34g,nyi,ij6g). (See Table 39). They are also much 
larger than those obtained from measurements of the sound velocity or 
from the heat of activation of the oscillations ; this is probably due to 
the fact that the molecules are in highly excited vibrational levels with 
v' <~ 26 instead of v' • — - 0. 

Table 39 

Transferring Cross Sections a of Rare Gases for the Visible 

Iodine Fluorescence 

(In cm 2 ) 

Gas He Ne A Kr Xe 

ct-10 16 113 159 240 309 480 

In general, Av does not exceed 1 or possibly 2 in an individual 
collision process. Bands originating from levels which are separated by 
several vibrational quanta from the initial level occur only if the 
excited molecules suffer a large number of collisions during their 
lifetimes. 

By using a spectrograph of very high resolving power, Wood and 
Loomis were able to prove that collisions with helium atoms always 
change the rotational quantum number/' by two units: every second 
line is missing in the bands of the fluorescence spectrum which is 
excited in iodine vapor by the green mercury line in the presence of 
helium at 10 mm. This is in perfect agreement with the theoretical 
expectations based on quantum mechanics (see Section 45) (igio). 

The ultraviolet resonance series of iodine vapor are not trans- 
formed into the complete band system by the addition of foreign 
gases; the series are only weakened more and more by increasing 
pressure of the foreign gas until they disappear completely. The same 
is true with respect to the Mc bands. Simultaneously, the "continuous 
bands" mentioned in Section 50, which are relatively weak in pure 
iodine vapor, are replaced by much stronger bands with a typical 
vibrational structure. According to Elliott, the region corresponding 
to the continua Y and X is covered by a single system in which he was 
able to measure 72 band heads represented by the equation : 



TRANSFERRING COLLISIONS IN IODINE VAPOR 195 

v = 33744 + 104(i;' + j)— 0.2(u' + J) 2 

— 214.26^" + i) + 0.592(w" + i) 2 

with v' varying from 1 to 12 and v" from 13 to 28. 

The lower state is supposed to be the electronic ground state with 
the vibrational frequency characteristic of the unexcited I 2 -molecule. 
The potential curve of the upper state must be shifted appreciably 
with respect to that of the ground state since transitions to the lower 
vibrational levels of this state do not occur. The band system becomes 
very complicated in certain parts because <a" is nearly equal to 2 co'. 

Elliott assumes that molecules which were raised by light ab- 
sorption to high vibrational levels of an electronic state X E+ are trans- 
ferred by collisions to low vibrational levels of this state and pass from 
there to a part of the potential curve of an electronic state 1 Z+ , 
situated immediately below the minimum of the potential curve of 
x 2"+ ; the fluorescence bands originate at the various vibrational levels 
of the state 1 Z+ (360). 

Although it is certain that a mechnism of this kind must be 
assumed for the production of the bands with vibrational structure, 
this assumption does not seem to explain why, in the absence of a 
foreign gas, the band should appear as continuous If the "continuum" 
corresponds to the same electronic transition, its emission must 
originate from approximately the same vibrational levels, since the 
wavelength range is the same in both cases The band can be made 
continuous only by the fact that in the absence of a foreign gas, much 
more numerous and densely packed rotational levels of 1 27+ are 
populated ; this is very improbable, because relatively sharp resonance 
spectra are emitted from the primarily excited state 1 Z+. If, on the 
other hand, the apparently continuous band originates from another 
electronic state, the latter might correspond to a repulsion curve and 
the band be really continuous 

The intensity distribution in the band observed in the presence 
of a foreign gas is independent of the wavelength of the primary radi- 
ation, but is influenced noticeably by the nature and pressure of the 
foreign gas and by the temperature. While the intensity of the 
short-wavelength bands of the system, corresponding to great values 
of v', decreases when the pressure of added nitrogen exceeds 10 mm, 
the intensity at the head of the system near 3450A increases continu- 
ously up to 760 mm N 2 . If the temperature is raised to 800° C, the 
short-wavelength part with greater v' values is enhanced. The 
intensity of the band system is much weaker and the intensity 



196 DIATOMIC GASES AND VAPORS 

distribution corresponds to a relatively greater population of the 
higher vibrational levels, when nitrogen is replaced by helium of the 
same pressure; with helium, the distribution is about the same at 
room temperature as it is with nitrogen at 800° C On the other hand, 
the u.v resonance series and the Mc bands are less strongly quenched 
by helium, which also, in this instance, has only a small efficiency in 
"transferring collisions," both for the transfer from one electronic 
state to the other and for transfers between the various vibrational 
levels of a given electronic state (jjj). 

On addition of nitrogen to iodine vapor, a structure similar to 
that of the band system at 3450A has been observed by Elliott in the 
other "continua" mentioned in Section 50; some of them are quenched 
again at higher N 2 -pressures. Nothing is known concerning the elec- 
tronic states from which they originate; apparently these states also 
lie somewhat below the state 1 Z+ which is reached directly in the 
process of excitation and have quantized vibrational levels. According 
to Elliott's analysis, their vibrational frequencies do not coincide with 
that of the system at 3450A (360). 

65. Quenching of Iodine Fluorescence by Foreign Gases. The 
quenching of the fluorescence of diatomic vapors may frequently be 
connected with chemical reactions, as was proved for the fluorescence 
of monatomic vapors. It is possible that the great quenching efficiency 
of gases such as oxygen and the halides is partly due to their chemical 
reactivity. However, very little is known about such processes and 
the particularly strong molecular fields of these electronegative gases 
also may favor induced predissociation. 

The "self-quenching" due to an increase of the vapor pressure of 
the electronegative gases themselves has frequently been overrated. 
It has already been mentioned that oxygen at atmospheric pressure 
and sulfur vapor at 250 mm exhibit strong resonance spectra. While 
bromine vapor was at first expected to be fluorescent only at the very 
lowest pressures because of its electronegativity, the red part of its 
fluorescence spectrum is, according to Plumley, not appreciably 
weakened by increasing the pressure to 70 mm. In Wood's earlier 
experiments, it seemed that the visible iodine fluorescence was com- 
pletely suppressed when the vapor pressure exceeded 1 mm ; a consider- 
able part of this apparent self-quenching was explained later by the 
fact that the effects caused by absorption processes were not taken 
into account. On the one hand, a smaller fraction of the incident light 
penetrates into the volume of the vapor, so that surface fluorescence 
becomes prevalent; and, on the other hand, the fluorescence light 



QUENCHING OF IODINE FLUORESCENCE BY FOREIGN GASES 197 

coming from the interior of the vapor is absorbed on its way to the 
exit window.* Actually, the resonance spectra produced by the 
radiation from a mercury arc are still observed as surface fluorescence 
of considerable intensity in iodine vapor saturated at 150° C (p ~ 
100 mm) (1223,1913). 
I Oil 



0.8 



0.6 



0.4 



0.2 













-\ y\\ 


\^2 


at O.I6mm 


h 




- \ \ 




^\-Av»i/ 






\ 






now 




N 8 at 0.02 

1 


7 mm l£-" 

1 


1 


A gr»en 

1 


1 



10 



Fig. 72. Quenching of the I 2 -fluorescence by 

foreign gases (I a -pressure 0.16 and 0.027 mm) [Berg (95)]. 

Ared, Ayellow, Agreen, quenching by argon of the 

red, yellow, and green part of the spectrum. 

Taking the absorption into account, the quenching half-pressure 
of the iodine fluorescence by iodine molecules is 0.08 mm. Because of 
the existence of this self-quenching action, the apparent quenching 
efficiency of foreign gases is largely dependent on the iodine vapor 
pressure itself: the higher the latter, the smaller the efficiency of the 
additional gas seems to be (Figure 72). The fluorescence intensities 
observed at increasing pressures of a foreign gas can be described by 

* Plumley seems to be of the opinion that without reabsorption processes 
the fluorescence intensity would not decrease at all with increasing vapor 
pressure, because a quenching proportional to the pressure would be exactly 
compensated by the growing absorption of exciting light, which is also pro- 
portional to the pressure. However, the amount of primary energy absorbed in a 
certain volume is proportional to the vapor pressure only as long as this pressure 
is so low that the reabsorption of the fluorescence light is of little importance. 
Once the absorption becomes strong, the assumption that the quantity of absor- 
bed radiation increases indefinitely with increasing pressure is erroneous (1243). 



198 



DIATOMIC GASES AND VAPORS 



means of a Stern-Volmer equation, but the half-pressure derived from 
the equation is not related to the natural life time of the excited 
molecules unless it is extrapolated to the iodine pressure zero. This 
has been done for the values given in Table 40. It appears that 
the simultaneous quenching by increasing I 2 -pressure and by addition 
of a foreign gas are not additive, as should be expected according to 
Equation (24), Section 35 (93). 

If the quenching of the visible iodine fluorescence is caused by a 
transfer of the excited molecules to a state represented by a repulsion 
curve, the relatively strong action of molecules of the same kind might, 
perhaps, again be explained by a quantum-mechanical resonance 
phenomenon in which the excited molecule returns to the ground state 
and another molecule is raised to the state of equal energy, but corre- 
sponding to the repulsion curve. 

The ultraviolet resonance spectra of iodine and the Mc bands are 
slightly weakened by increasing vapor pressure; the self-quenching 
becomes less effective, with increasing wavelength of the exciting light. 
The resonance progression excited by the mercury line 2537A is still 
very strong and shows a practically unaltered structure at a saturation 
pressure of two atmospheres. Very few molecules are in the high 
vibrational state from which the line 2537 can be absorbed, and, there- 
fore, the corresponding "resonance effect" which could produce 
quenching should be very weak. 

The conclusion that the quenching of the visible iodine fluo- 
rescence is actually due to a predissociation process was derived by 
Loomis and Fuller from absorption measurements. The absorption in 
the bands corresponding to values of v' > 12 increases considerably on 
addition of argon or oxygen to the iodine vapor, and this phenomenon 
can be ascribed only to a broadening of the individual lines caused by 
the fact that the average life of the excited molecules is shortened by 
induced predissociation (801,955,1715,1717). 

Table 40 

Quenching of the Visible Iodine Fluorescence 

Bands by Collisions 



Quenching gas 


Hef 


At 


H 2 


o 2 


co 2 


Ether 


Cl 2 


h 


Half-value 
pressure p* in 
mm 


70(20) 


6 (2.3) 


5 


3.5 


1.2 


0.3 


0.2 


0.08 



fThe first figures relate to the red, the second, in ( ), to the green part of the 
fluorescence spectra. 



QUENCHING OF IODINE FLUORESCENCE BY MAGNETIC FIELDS 199 

Furthermore, lines characteristic of atomic iodine appear in the 
absorption spectrum of a mixture of iodine vapor and argon under the 
action of strong irradiation with light from which all wavelengths 
below 5100A are filtered out, while these atomic lines occur in pure 
iodine vapor only if the vapor is directly photodissociated by light of 
wavelength below 5000A (1717)- 

According to Rabinowitch and W. C. Wood, the photodissociation 
of I 2 -molecules is produced with the same high yield of almost 100 % 
if it is caused by light absorption in the continuum adjoining the con- 
vergence limit, or if it is due to absorption in the different parts of the 
discontinuous bands between the blue-green and the yellow in the 
presence of a foreign gas of a few hundred mm (He, A, H 2 , or N a ). The 
relative number of dissociated molecules was determined by the 
decreasing absorption in the characteristic molecular bands, and 
every absorption process in the continuous band was assumed to 
produce dissociation. These experiments prove that the quenching 
action of the various gases is due almost exclusively to induced 
predissociation of the excited molecules, but considering the high 
pressure of the quenching gas at which each excited molecule 
undergoes many collisions during its lifetime, they do not answer the 
question whether the probability of a transfer from the excited state 
into the state of repulsion depends on the wavelength of the exciting 
light. This problem will be dealth with in the next section (1318). 

66. Quenching of Iodine Fluorescence by Magnetic Fields. Further 
information regarding the mechanism of the quenching processes has 
been gained by experiments proving the influence of strong magnetic 
fields on the intensity of the fluorescence, and the interpretation of 
these experiments by Turner and van Vleck. According to Steubing's 
early investigations, the intensity of the iodine-vapor fluorescence 
excited by white light is considerably weakened by a magnetic field; 
the bands in the green part of the spectrum are more strongly affected 
than the red ones. It has since been proved repeatedly that this effect 
is not caused by a corresponding change in the absorption spectrum 
of the vapor {1162,1170,1576, 1577). If a resonance spectrum is excited 
in I 2 -vapor by monochromatic light, the two components of every 
doublet and the various members of a simple resonance progression 
are weakened to the same extent. However, the total intensities of 
resonance spectra excited by different primary lines are reduced in 
different degrees by a given magnetic field: the quenching efficiency is 
related to the vibrational quantum number v' of the excited electronic 
state. Fig. 73 shows the relative weakening I m /I as a function of the 



200 



DIATOMIC GASES AND VAPORS 



wavelength of the exciting light in a field of 12,500 gauss. A fairly 
smooth curve can be plotted through the observed points ; since these 
points correspond to widely different values of the rotational quantum 

number J', evidently only the 
values of v' and not those of J' 
are decisive for the effect (1713, 

1743)- 

The quenching reaches its 
maximum at the frequency 1 8,500 
cm -1 . According to theory, this 
frequency corresponds to the 
value of v' at which the potential 
curve A of the excited molecule 
intersects the repulsion curve C; 
it is the point where the induced 
predissociation has the greatest 



1.0 



'0.8 



0.6 



0.4 













- 


A 




1 > 


1 


- 


\ 




Y 




- 




***-■*; 







16000 



18000 
v, cm" 1 



20000 



Fig. 73. Quenching of the la-fluore- 
scence by a magnetic field . [Turner 
(1713)1 



probability. Van Vleck's theory for predissociation induced by mag 
netic fields leads to the equation : 



A =(7 -/ m )/i = 6HV + 6H2) 



(54) 



n which H is the magnetic field strength, b a constant depending on 
v', and a = 1/t the reciprocal lifetime of the excited state. Genard 
measured the effect for two doublets of the resonance series excited 
by the green mercury line and obtained a satisfactory agreement 
between his observations and Equation (54), at least for values of H 
larger than 20,000 gauss. Scholz confirmed his results also for weaker 
fields down to 10,000 gauss {482,484,1234,1475). 

It might be expected that the induced predissociation of excited 
I 2 -molecules by collisions and by magnetic fields should show the 
same dependence on the wavelength of the exciting light, viz., the 
value of v'. However, in contrast to the clean-cut results obtained for 
the magnetic effect, the influence of v' on the quenching by collisions 
is very uncertain, according to investigations by several authors." An 
observation published by Ramsauer, according to which the individual 
members of a homogeneous resonance spectrum suffer unequal losses 
of intensity by collision-quenching, also needs confirmation ( 13 30, X714). 

Berg has investigated the simultaneous quenching by collisions 
and by magnetic- fields. At increasing iodine vapor pressure the 
quenching action of a given magnetic field decreases continuously; it 
is much less noticeable at room temperature than at 0° C (p = 0.03 



TRANSFERRING COLLISIONS AND INDUCED PREDISSOCIATION 201 

mm) and vanishes almost completely at 40° C (p = 1.2 mm). As in 
the case of simultaneous quenching by a foreign gas and by an in- 
crease of the I 2 vapor pressure, this result is explained by the shorter 
lifetime of the excited molecules in I 2 -vapor of great density. Actually, 
the effect of the magnetic field is even less reduced by the quenching 
interaction of the iodine molecules than would be expected according 
to an additive superposition of the two factors. The same is true if a 
magnetic field is applied to the iodine fluorescence already weakened 




I -pressure in mm 



- pressure in mm 



Fig. 74. Simultaneous action of collisions and a magnetic field 
on the I 2 -fluorescence- (Berg). 
a: variable I 2 -pressure 
b: variable 2 -pressure at I 2 -pressure of 0.17 mm. 

H: 20,000 gauss. /: fluorescence intensity without field. 
Im : intensity with field. 



by the presence of a foreign gas. This is shown in Figure 74, where the 
solid curve represents the measurements, while the broken curve is 
calculated by superposition of the two individual effects. It seems that 
the magnetic field, in addition to its own quenching action, deforms 
the potential curves of the excited molecules in such a way that the 
effective cross sections for the quenching collisions become larger 

(93)- 

67. Transferring Collisions and Induced Predissociation in Other 

Diatomic Molecules. The predominance of either transferring collisions 
or of induced predissociation depends mainly on the shape of 'per- 
turbing potential curves and on their location with regard to the po- 
tential curve of the excited state (592). In the fluorescence of S 2 , for 
instance, the quenching is comparatively weak, and transferring col- 
lisions are frequent; the molecules of Se 2 and Te 2 show the opposite 
behavior. 

Two characteristic regions of predissociation are produced in the 
absorption spectrum of S 2 by the existence of two perturbing curves 



202 



DIATOMIC GASES AND VAPORS 



C and C (Figure 75). Thus, the relatively weak quenching of the 
S 2 -fluorescence is not caused primarily by a selection rule (as in the 
case of the visible I 2 -fluorescence), but must be explained by the fact 
that the intersection point of curve A with curve C lies too high (near 
v' = 19) and, therefore, the energy necessary for raising a fluorescent 
molecule to this point is practically never available in a collision.* 
Curve C, on the other hand, has a shallow minimum, and its inter- 
section point with curve A lies below the dissociation level of the 

weakly bound state represented 
by C Radiating transitions from 
C to the ground state have never 
been observed. Therefore, a tran- 
sition from A to C frequently 
will be followed, after a few os- 
cillations, by a return to some 
vibrational level of A, and such 
collisions by which an excited 
molecule is transferred from A 
to the state C would produce 
the same overall result as a 
normal "transferring" collision. 
Some quenching may occur ne- 
vertheless, because of the pos- 
sibility of the dissociation of the 
loosely bound molecule in the 
state C by a collision before its 
return to the state A. The fact 
that transitions A -+ C are induced by collisions is again proved by 
a change in the absorption spectrum; while the spontaneous predis- 
sociation bands are limited to the region close to v' = 9, the bands 
corresponding to values of v' down to 4 become diffuse in the presence 
of a foreign gas (1380). 

According to Durand, the transferring and the quenching effi- 
ciency of all rare gases for S 2 -molecules in the vibrational level v' = 8 
are of the same order of magnitude, and they are also about the same 
for a change in the rotational and the vibrational energy; the trans- 
ferring efficiency of helium is greater than that of the heavier rare 
gases while its quenching efficiency is smaller. Finally, Durand finds 

* No fluorescence is excited in S 2 -molecuIes by absorption of lines by which 
the molecules are raised into levels of the excited electronic state with v' ~>_ 17, 
e.g., by absorption of the Mg-line 2800A. 



40 000 



30 000 



20 000 



10 000 




Fig. 



75. Potential curves 
(Rosen) . 



of S„ 



TRANSFERRING COLLISIONS AND INDUCED PREDISSOCIATION 203 

that the apparent quenching cross section of all rare gases decreases 
considerably with increasing pressure of the rare gases or with in- 
creasing number of excited molecules which have already been trans- 
ferred by a collision into a lower vibrational level. The half-pressure 
calculated from the quenching at a helium pressure of 8 mm is 
p* = 12 mm ; from the relative intensity observed at a helium pressure 
of 46 mm, the value p* = 37 mm is derived. However, even this value 
is still so far below those obtained by earlier investigators, who found 
for the quenching of the S 2 -fluorescence by helium p* > 400 mm, that 
it is doubtful whether the discrepancy can be explained by the fact 
that in these experiments the fluorescence was excited by white light 
and that, therefore, the bands belonging to small values of v' pre- 
vailed (325). 

The far larger quenching efficiency of helium and other gases for 
the fluorescence of Te 2 (and similarly of Se 2 ) is easily understood from 
the potential-curve diagram of Figure 70. The transition probability 
corresponding to spontaneous predissociation is greatly enhanced by 
collisions. Induced predissociation prevails so strongly in comparison 
with transferring collisions that even at high helium pressures only 
the bands which originate from the level reached by a single transfer 
with Av = 1 appear in the Te 2 fluorescence spectrum in addition to 
the resonance series which have been directly excited (473,592). 

The action of magnetic fields on the fluorescence of the vapors of 
S 2 , Se 2 , and Te 2 is still somewhat doubtful. According to Genard, 
several resonance series of S 2 (for instance, the double progression 
excited by the mercury lines 3126 and 3131 A) and of Se 2 are enhanced 
by the influence of a magnetic field, while others are weakened (484, 
485,1234,1520). An increase in intensity of a series can be caused 
exclusively by a greater number of the molecules in the level v'J' 
from which the emission of the series originates; either a smaller 
fraction of these molecules is deactivated by competing radiationless 
processes (this is out of the question since no quenching processes 
occur in the absence of the magnetic field), or more excited molecules 
are produced; this can occur if the absorption of the exciting line is 
increased by the Zeeman effect of the absorption band.* If an en- 
hancement of a resonance scries by a magnetic field must be explained 
by an effect of this type, the same interpretation can also be used to 

* In a region of induced predissociation, the magnetic perturbation of the 
potential curves and, thus, the Zeeman effects of the band lines are particularly 
large. Due to the displacement or broadening of the lines caused by the Zeeman 
effect, the absorption of a given exciting line can be increased or decreased. 



204 DIATOMIC GASES AND VAPORS 

account for the weakening of other series. Nevertheless, the mecha- 
nism assumed for interpreting the magnetic quenching of the I 2 - 
fluorescence may also have a part in the weakening of some of the 
resonance spectra of Se 2 and Te 2 . Since most of the resonance series 
consist of complicated groups originating from a number of closely 
adjacent absorption lines, the changes in intensity can be different 
for various members of the spectrum because of an unequal "fine 
structure" of each group {25). 

The fluorescence of the diatomic radicals HgCl, HgBr, and Hgl 
can be excited by photodissociation of the mercuric halides by short- 
wavelength u.v. radiation. In the fluorescence spectrum of Hgl a 
system of bands (the so-called S-bands) reaches from 4425A more or 
less into the u.v., according to the wavelength of the exciting radiation; 
'the corresponding vibrational levels of the excited radicals are 
characterized by lower or higher values of v'. In the absence of a 
foreign gas, the short-wavelength limit of the emission band lies at 
3100A, if the fluorescence is excited by an Al-spark (A < — > 1860A), and 
at 3800A under excitation by a Zn-spark (A ~ 2150A) On addition 
of a foreign gas, both quenching and transferring collisions occur. 
With Al-spark excitation, all bands corresponding to v' > 1 1 are 
suppressed by the presence of argon or nitrogen, while in the other 
parts of the band system the effect of transferring collisions prevails so 
much that the visible fluorescence even becomes appreciably brighter. 
If only the long-wavelength bands are excited by the Zn-spark, the 
visible fluorescence is not affected noticeably by an admixture of A, 
N 2 , or CO, whereas it is strongly quenched by 2 and H 2 . The bands 
below 4000A are weakened also in this case by the "non quenching" 
gases. Simultaneously, the structure of the spectrum, which is extreme- 
ly complicated when many levels of the upper electronic state con- 
tribute to the emission, is greatly simplified and consists now in the 
main only of the progression 0' -»• 0", 1", 2" . . . so that the analysis 
becomes much easier {1836-183C)). 

Analogous effects are obtained with mercurous bromide and 
chloride. In the presence of nitrogen at 100 mm, even the weak bands 
of the isotope HgCl 37 , which otherwise are completely submerged in 
the bands of the more abundant HgCl 35 , can be clearly identified. 

A second band system, C (3100-2800A), showing fine structure, 
occurs in the fluorescence spectrum of Hgl when it is excited by the 
Al-spark. Only quenching, and no transferring, collisions are produced 
in this system by foreign gases. The quenching cross sections of various 
gases for band C are listed in Table 41. The quenching efficiency of 



TRANSFERRING COLLISIONS AND INDUCED PREDISSOCIATION 205 



2 is the same for the bands corresponding to v' = 5 and v' = 1. Table 
41 shows that the quenching efficiency depends on the molecular 
fields as well as on the masses of the quenching molecules. On the other 
hand, the efficiency of all gases is largest for the fluorescence of Hgl, 
smaller for HgBr, and smallest for HgCl. The abnormally great 
quenching cross section of NH 3 for the three halides is caused by a 
chemical reaction: the ammonia pressure decreases after strong 
irradiation, probably because of the formation of ammoniates (1661) . 



(P* 



Table 41 

Quenching of the U.V. Fluorescence of Hg I 

half -value pressure in mm; a q and a k = quenching and kinetic 
cross sections) 



Quenching gas 


NH, 


o 2 


co 2 


N, 


CO 


H 2 


A 




p* 


— 


26 


38 


50 


53 


30 


100 


Band C 


O g -10™ 


37 


28 


22 


14 


13.4 


0.4 







GqlOk 


1.74 


0.93 


0.64 


0.41 


0.43 


0.23 


— 


Band B 


(7 ? -10 16 


185 


31.5 


— 








0.35 


— 



The fluorescence band of the radical CN at 3883A exhibits widely 
different rotational-energy distributions according to the wavelength 
of the light by which the parent molecule ICN or C 2 N 2 is dissociated ; 
they correspond to a "rotational temperature" of the vapor of about 
1500° K {K' ~ 16) or 150° K 
(K' <**> 5), respectively, as com- 
pared to the average temperature 
of the vapor of 380° K (K' ~ 8). 
By the admixture of foreign gases, 
the normal distribution of the ro- 
tational energy is restored, and the 
curves of Figure 76 show that in this 
case the mass of the colliding par- 
ticles plays the most important part. 
The relatively small difference be- 
tween the curves for argon and for 
nitrogen and carbon monoxide may 
be due to the existence of a simul- 
taneous quenching action of N 2 and 
and CO, of which no account has 



15 



10 



^ 






\\p 






- 


• • 




i 


i 



50 100 

p in mm 



Fig. 76. Influence of foreign 
gases on the rotational struc- 
ture of CN band at 3883A 
( Jakowlewa) : A{»); N 2 (A); 
CO(o); H 2 (A). 



206 DIATOMIC GASES AND VAPORS 

been taken in the measurements ; the small efficiency of hydrogen is 
quite obvious (681,683,684). 

Characteristic bands of the radicals HgH and OH can be excited 
as sensitized fluorescence in mixtures of mercury vapor with nitrogen 
and hydrogen or with water vapor. The OH-bands are also produced 
by photodissociation of various polyatomic compounds (see Sections 
74 and 94). In all these cases, the bands show an abnormal rotational 
intensity distribution : the high rotational levels have not only a much 
larger population than corresponds to the actual temperature of the 
vapor, but the relative population of the various levels does not 
correspond to any Maxwellian distribution. For the HgH-bands, the 
addition of nitrogen increases the relative intensity of the tail of the 
band v' = 0-W =0 and, accordingly, the number of molecules of 
high rotational energy in the level v' = 0. The excitation process 
produces HgH-molecules in vibrational levels up to v' = 5, as is 
proved by the presence of the bands 5' -> 1" and 4' -* 0" (2878 and 
2838A) in the fluorescence spectrum. These bands disappear completely 
at higher N 2 -pressures ; the HgH-molecules are transferred by col- 
lisions into lower vibrational levels of the excited electronic state, and 
the vibrational energy is transformed into rotational energy in this 
process. Genuine quenching is negligible; it is hardly noticed at a 
N 2 -pressure of 160 mm. The higher vibrational levels of HgH* are 
depopulated also by collisions with H 2 0-molecules. In this case, 
however, the lost energy is taken up, in the main, by the colliding 
H 2 0-molecules, so that the increase of rotational energy in the HgH- 
band 0' -> 0" is relatively small; on the other hand, a direct decrease 
of rotational energy by collisions with water molecules does not seem 
to be considerable. 

In the mercury-sensitized fluorescence of OH, the bands 0' -* 0" 
at 3064A, l'->0" at 2811 A, and l'-»- 1" at 3122A are observed, all 
with abnormally large quantum numbers /'. In this case, no en- 
hancement of the rotational energy is caused by collisions with N 2 - 
molecules, but the weakening of the bands originating from the level 1 ' 
is relatively much greater than the decrease of intensity of the lines 
which correspond to high /' values in the band 0' -> 0"; the collisions 
cause the transfer 1 ' -> 0' with greater probability than a decrease of 
J'. It is possible, however, that the latter effect is compensated for, 
in part, by the repopulation of the high rotational levels accompanying 
the loss of vibrational energy. At any rate, such processes are much Jess 
frequent in the collisions of OH* with N 2 than in the case of HgH* 
(io6,g63,g64,nji,i365,a,b). 



ATOMIC FLUORESCENCE CAUSED BY INDUCED PREDISSOCIATION 207 

68. Atomic Fluorescence Caused by Induced Predissociation. Re- 
sonance series in the blue-green band system of Na 2 , in sodium vapor 
saturated at 300° C, are appreciably weakened by the addition of 
helium ; the decrease of intensity is the larger, the higher the vibrational 
level v' from which a progression originates. For instance, the series 
excited by the Zn-line 4722 (v' = 9) is more strongly quenched than 
the series excited by the Zn-line 481 1A (v' = 4); the effect is almost 
negligible for the fluorescence excited by the Mg-line 5183A (»' = 2). 
The weakening of the resonance spectra is not compensated by the 
emission of other bands of the system caused by the transfer of excited 
molecules into adjacent vibrational levels. Instead of this effect, the 
D-lines, which are absent from the monochromatically excited 
resonance progressions, appear in the fluorescence spectrum; their 
intensity is the stronger, the greater the value of v' and the more, 
accordingly, the corresponding resonance series is quenched. Ap- 
parently the sodium molecules in high vibrational levels of the excited 
electronic state are dissociated by the collisions into two sodium 
atoms Na (3 2 S) and Na (3 2 P), the latter subsequently being able to 
emit the atomic resonance lines. In an inelastic collision the helium 
atoms transfer, because of their small mass, 92% of the relative 
kinetic energy into internal energy of the Na^-molecule ; at 300° C, 
2 % of all atoms have sufficient kinetic energy for dissociating Na^- 
molecules in the vibrational levels v' = 4; and 10% even have the 
energy for dissociating molecules with v' = 9. Since no stepwise 
transfer of vibrational energy with Av = 1 seems to occur, it is very 
improbable that complete dissociation is produced by a summation of 
such processes. It is more likely that the effect is produced by a direct 
transition into another potential curve corresponding to a state of 
repulsion, as indicated by the dotted line C in Figure 68A (675). 

Addition of argon or nitrogen causes, qualitatively, the same 
effect. However, while the molecular fluorescence is much more 
effectively quenched, especially in the case of nitrogen, the simul- 
taneous emission of the D-lines is much weaker. This may be due to a 
direct quenching of the band fluorescence by another mechanism (for 
instance, dissociation into two unexcited Na-atoms or a chemical 
reaction), or to a secondary quenching action on the excited sodium 
atoms which have been produced by a first collision. An increase of the 
sodium vapor pressure itself to 50 mm (saturation pressure at 600° C) 
causes a very strong emission of the D-lines under otherwise identical 
conditions of excitation. It is possible that in this case the mechanism 
is of the same nature as the one produced by helium; but it can also 



208 DIATOMIC GASES AND VAPORS 

be a kind of sensitized fluorescence in which the excited Na 2 -molecules 
transmit their electronic energy to colliding sodium atoms (778). 

G. Photodissociation of Diatomic Molecules Followed 
by Atomic Fluorescence 

69. Products of Photodissociation. The products of photodissoci- 
ation of diatomic molecules are either two neutral atoms in the ground 
state, or a positive and a negative ion, or, most frequently, two neutral 
atoms of which at least one is in an excited electronic state. In a 
molecular absorption spectrum each of these dissociation processes 
corresponds to a continuous band in a different spectral region ; some 
of these bands may overlap. 

The continuum adjoining the visible band system of I 2 is related 
to the dissociation of the molecule into I( 2 P 3/2 ) and I( 2 Pi /2 ). Since one 
of the atoms is in the ground state and the other in a metastable state, 
no emission of light follows the dissociation process (233,337). 
However, iodine vapor has other absorption bands reaching far into 
the u.v., and on irradiation with light of wavelengths below 1450A the 
vapor emits the resonance line of monatomic iodine at 2063A. Probably 
the molecules are dissociated into a normal atom and an atom in the 
state 3 S 1 i 2 . 

The convergence limit of the blue-green band system of Na 2 lies 
at 4565A. R. W. Wood observed a strong emission of the D-lines by 
sodium vapor saturated at 400° C, when it was irradiated with light 
of wavelengths below 4500A. The dissociation process induced by light 
absorption in the continuum adjoining the blue-green band system is 
represented by the equations (1908) : 

Na 2 + ftv -» Na (3 2 S) + Na (3 2 P); Na (3 2 P) -> Na (3 2 S) + hv D 

70. Dissociation of Metal Halides and Their Heat of Dissociation. 

The excited electronic states of the halides of silver and thallium from 
which resonance fluorescence can originate dissociate into a normal and 
a metastable atom: Agl into Ag (55) + I ( 2 P 1/2 ) and Til into Tl 
(6 2 P 1/2 ) + I ( 2 P 1/2 ) or Tl (6 2 P 3/2 ) + I ( 2 P 3/2 ); Tl ( 2 P 3/2 ) and I ( 2 P 1/2 ) 
are metastable and have nearly equal energies. It has already been 
mentioned that, in contrast to the silver halides, the first excited state 
of thallium halides is very loosely bound. The alkali halides have no 
stable excited states at all; they form stable molecules only in the 



DISSOCIATION OF METAL HALIDES AND HEAT OF DISSOCIATION 



209 



Cs (60) + I 



ground state, as so-called ionic molecules. All higher electronic states 
are represented by pure repulsion curves (Figure 77). Accordingly, the 
absorption spectra consist exclusively of continuous bands in which no 
fluorescence can be excited. Light absorption in the first and in the 
second absorption band splits the molecules into two neutral atoms in 
the ground state or into a positive metal ion and a negative halide ion, 
respectively. 

By light absorption in continuous bands situated in the far u.v., 
the halides of the heavier metals, as well as those of the alkali metals, 
are dissociated into a normal or a 
metastable halide atom and an ex- 
cited metal atom. Several continua 
have been observed in the u.v. ab- 
sorption spectra of every compound ; 
Figure 77 shows six bands of this 
type for Csl which could all be as- 
cribed to different dissociation pro- 
cesses [1093,1461). However, not 
more than two atomic emission lines 
were obtained, so far, from any of 
the dissociated compounds. If the 
vapor of - sodium iodide is irradiated 
with light of a wavelength near 
2450A, only the D-lines are emitted 
in the fluorescence spectrum; under 
the action of light with A < 1850A, 
the second member of the principal series at 3303A, also appears. The 
fluorescence of silver iodide vapor, irradiated with light of wavelengths 
between 2115 and 2060A, exhibits almost exclusively the long-wave 
component of the Ag resonance doublet (3383 A), whereas with 
primary wavelengths below 2060A the short -wavelength component 
(3280A) predominates. In the first case, the dissociating silver atoms 
are all in the state 5 2 P 1/2 ; in the second, most silver atoms are in the 
state 5 2 P 3/2 . The atomic lines (X F ) excited in various vapors by this 
process and the maximum wavelengths (X m ) of the exciting radiation 
are listed in Table 42 {191,276, 800,1267(1,1634,1635,1637, iyj3~ijy6). 
In general, the spectral region and the long wavelength limit within 
which the atomic resonance lines can be excited, have been determined 
using a number of spark lines between 2400 and 1850A. The yield as a 
function of the wavelength of the exciting light has been measured 
quantitatively only for the D-line fluorescence of Nal and the green 




Fig. 77. Potential curves of Csl 
(Mulliken). 



210 



DIATOMIC GASES AND VAPORS 



Tl-fluorescence of TIL Figure 78 shows that the curve for the fluo- 
rescence yield and the absorption curve do not coincide ; one or several 
other processes must be produced by the absorption apart from the 
excitation of fluorescence. According to Terenin, one of these processes 
corresponds to the dissociation of Til into the ions Tl + and I - . Curve 
II in Figure 78 represents the excitation spectrum of the green fluo- 













■\ 


^ 


i^V, 






\ 


\ 

\ 




VSq 





1900 



2000 



2100 



2200 



2300 A 



Fig. 78. Excitation spectra (broken line) of Til photodis- 

sociation (Frank) . The continuous line in the absorption 

spectrum. 

I: Tl* + I. II: (Tl + + I~). Ill: undetermined. 



rescence, and curve I the band in which the dissociation into ions 
occurs* (38g, 432, 1643). 

If the wavelength of the exciting light is appreciably smaller than 
X m in Table 42, the atomic fluorescence lines (for instance, the D-lines) 
are broadened by the increasing Doppler effect. If Nal-molecules are 
dissociated by irradiation with the Zn-line 2026A, the width of the 
D-lines is 0.1 A as compared to the normal Doppler width of 0.03A at 
the temperature of observation. (Compare Section 20.) The velocities 
of the excited atoms determined by the Doppler-effect broadening 
have no preferential angular distribution with respect to the direction 
of the primary light (622,1036). 

The last two columns of Table 42 give the heat of dissociation D 

* Terenin is of the opinion that some Til fluorescence bands mentioned in 
Section 61, which are excited by light absorption in the spectral region I, are 
caused primarily by this dissociation process and a subsequent recombination. 
However, this hypothesis is far from being convincing. The bands consist of 
two strong maxima at 4439 and 4084A with adjoining fluctuations which are 
also observed in the normal absorption spectrum of Til. Absorption of light of 
wavelength < 1900A produces an additional continuous fluorescence band 
between 4000 and 5000A (maximum at 4152A) which coincides with the absorpt- 
ion bands mentioned in Section 61, and, finally, a narrow linelike band at 3475A. 



DISSOCIATION OF METAL HALIDES AND HEAT OF DISSOCIATION 



211 



Table 42 
Photodissociation of Diatomic Vapors of Metal Halides 









Heat of dissociation in eV 


Compound 


Ap in A 


X m in A 










Calculated 


Thermochemical 


Lil 


6706 


2350 


3.4 


3.45(2.8) 


Nal 


5892 


2450 


2.95 


3.1 (2.99) 




3303 


1854 


2.93 




Rbl 


7947/7800 


2650 


3.00 


3.32(3.48) 




4261/01 


2080 


3.08 




Csl 


4555/93 


2085 


3.22 


3.31(3.6) 


LiBr 


6706 


2040 


4.2 


4.45(3.6) 


NaBr 


5892 


2144 


3.65 


3.78(3.7) 


Agl 


3383 


2115 


2.2 


(2.0) 




3280 


2060 


2.1 




Cul 


3274/47 


2170 


1.92 


(1.4) 


Til 


5351 


2080 


2.65 


(2.0) 


TIBr 


5351 


1915 


3.21 


(2.8) 


T1C1 


5351 


1850 


3.4 


(3.4) 


Bil 


3068 


2100 


2.04 





derived from the fluorescence experiments and from thermochemical 
data. The minimum energy needed for the photodissociation process 
is calculated from the value of X m ; the energy liberated by the emission 
of the fluorescence line X F is known. D is obtained as the difference of 
these two energies. 

This method of determining the heat of dissociation is far less 
reliable than other spectroscopic methods and furnishes hardly more 
than a rough approximation. On the one hand, the minimum energy 
corresponding to X m may be appreciably larger than the dissociation 
energy if, according to the F. C. principle, the transition to therepulsion 
curve can occur only with a simultaneous transfer of kinetic energy 
(Figure 59). On the other hand, the experiments are performed, in 
general, at an elevated temperature in order to obtain a sufficient vapor 
pressure. The higher this temperature, and the greater the pressure, 
the more numerous are the molecules which are in higher vibrational 
levels of the electronic ground state and the smaller, therefore is the 
additional minimum energy which must be supplied for the dissoci- 
ation. Thus, the. following values of X m were obtained by Visser for 
the excitation of the green fluorescence in Til-vapor (Table 43) {1775). 
In spite of these objections against the method, its results are in 
satisfactory agreement with the thermochemical data, inasmuch as 



212 DIATOMIC GASES AND VAPORS 

Table 43 

Values of X m for the Excitation of the 
Green Fluorescence in TII-Vapor 

(T 1 and T 2 : temperature regulating the 

pressure and temperature of observation 

chamber, respectively) 



r, r cj 


T, (° C) 


Kn in A 


385 
385 
385 

465 


401 
595 
720 
620 


2100 
2144 
2200 
2313 



the latter are not very consistent among themselves, if they are taken 
from different sources. The figures in parentheses in Table 42 are 
those listed in the International Critical Tables ; the others come from 
more recent publications 



H. Lifetime of the Excited States and Polarization 
of the Resonance Spectra 

71. Lifetime. The lifetime of the excited state from which reso- 
nance spectra originate has been determined by means of a fluo- 
rometer for the green-yellow Na 2 -bands ; the measurements, which do 
not seem to be quite reliable, gave a value of t = 10 -8 sec (642). All 
other experiments, dealing chiefly with the visible fluorescence of I 2 (e.g., 
displacement of the fluorescence in a vapor jet, broadening of a sharply 
denned fluorescent beam by Brownian movement, and also a fmo- 
rometric determination), gave no positive results, or, at best, an upper 
limit for t which, in all experiments, was of the order of 10 -6 sec. 
About the same value was obtained by applying the Stern-Volmer 
equation to the self-quenching of the iodine fluorescence and assuming 
a quenching efficiency of 100 % for gas-kinetic collisions. However, the 
calculations were based on measurements of the self-quenching in 
which the influence of increasing light absorption was not taken into 
account (see Section 65) and, therefore, have no great value. They lead 
to the conclusion that in order to obtain "reasonable" lifetimes of the 
order of 10~~' to 10 -8 sec, one has to assume effective quenching cross 
sections which are much larger than the kinetic cross sections. On 
the other hand, Heil explained the high sensitivity of the excited 



THEORY OF THE POLARIZATION OF RESONANCE SPECTRA 213 

I 2 -molecules to self-quenching by their relatively long lifetime, which 
is due to the fact that the bands correspond to a triplet-singlet inter- 
combination transition. This proves once more that one of the two 
independent parameters contained in the Stern- Volmer equation 
must be determined by another method (5g2,i5ji,igi3). 

Finally, it has been shown that data concerning the lifetime of 
excited diatomic molecules cannot be obtained by observing the 
influence of temperature or of magnetic fields on the polarization of 
the resonance radiation (compare the following section) (1275). 

72. Theory of the Polarization of Resonance Spectra. While it 
remained doubtful for a long time whether the resonance radiation of 
monatomic vapors was polarized or not, Wood ascertained immediate- 
ly after the discovery of the resonance spectra of iodine and sodium 
vaporthatthe radiation showed a partial polarization if the fluorescence 
was viewed in the direction perpendicular to the direction of the pri- 
mary light. In the case of diatomic molecules perturbations by weak 
magnetic fields or neigboring molecules are almost negligible, and, 
therefore, the phenomenon could be observed without taking any 
special precautions (1864,1878). 

In atoms, the electronic orbits have no preferential orientation 
in a field-free space ; they are degenerate with regard to their spatial 
quantization and very weak external forces are sufficient for influencing 
their orientation in space. In a diatomic molecule, the electronic orbits 
have a well-determined orientation with respect to the line joining the 
atomic nuclei, from which they are only very little deviated even by 
large external forces; the Zeeman effects of band lines are very 
small. In order to alter the spatial orientation of the electronic orbits, 
the orientation of the whole molecule, including the heavy nuclei, 
must be changed. 

As long as the problem could not be interpreted by quantum 
mechanics, the most plausible assumption was to treat the molecule as 
a more or less anisotropic classical oscillator. For complicated poly- 
atomic molecules, this is still the only possible model and it will, there- 
fore, be dealt with in more detail in a later section. In the simplest 
case, the oscillators are completely anisotropic (linear); the distri- 
bution of their spatial orientation is at random in a gas. If, under these 
conditions, the oscillators are irradiated with plane-polarized light, 
the fluorescence which they emit in a direction perpendicular to the 
primary light has a degree of polarization p p = 50 %,* as long as the 

* If the incident radiation is unpolarized, the polarization of the fluo- 
rescence light in the direction perpendicular to the primary light is 
Pringsheim 8 



214 DIATOMIC GASES AND VAPORS 

oscillators are! at rest. The degree of polarization is reduced by the 
thermal agitation of the molecules. 

The translational component of the thermal agitation obviously 
does not affect the orientation of the oscillators and the polarization 
of the fluorescence. The latter is reduced by the rotational component, 
but not completely destroyed, if the axes of rotation retain their 
direction, i.e., if no perturbing collisions occur during the emission 
process. The frequency of molecular rotation is, in general, of the order 
of 10 u sec -1 . Since the lifetime of the excited states is equal to or 
larger than 10 -8 sec, each molecule performs a great number of rotations 
during its lifetime. Under these circumstances and with plane polari- 
zation of the primary light, the polarization corresponding to com- 
pletely anisotropic oscillators is p p = 14.3 %. A further increase of the 
rotational velocity by an increase of temperature has no influence upon 
these relations and, therefore, no conclusions can be derived from such 
experiments with regard to the value of r {1275). 

In the quantum-mechanical treatment of the problem, which was 
developed by Placzek and by Mrozowski, the principle of spectro- 
scopic stability was again applied (compare Section 28) : in a field-free 
space the polarization of the fluorescence is the same as in a strong 
magnetic field by which the symmetry of the system is not altered. 
Although the absolute values of the Zeeman separations of the 
magnetic sublevels remain very small even in a field of considerable 
strength, each term, with the exception of 27-terms which are not 
affected, splits into 2J — 1 sublevels with different magnetic quantum 
numbers m, J being the -quantum number of the total angular mo- 
mentum. As for atomic lines, the degree of polarization of the mole- 
cular fluorescence is derived from the relative population of the 
individual Zeeman levels of the excited state, which is determined 
by the special experimental conditions* and by the probability of the 
several transitions which can occur between these levels and the 
various Zeeman levels of the electronic ground state. Again, Am = 
corresponds to 77-components and Am = ± 1 to ^-components. J 
depends on the nature of the electronic term and on the molecular 
rotation but is independent of the nuclear vibration. Therefore, the 

Pn = Pplfi — Pp) ■ thus - for Pp = 50 % ; Pn = 33 %- The relation holds, however, 
for every degree of polarization pp. Where the distinction between pp and p n 
is not to be emphasized, the simple symbol p is used for pp. 

* These are the directions of the exciting radiation, the electric vector in 
this radiation, and the magnetic lines of force, with respect to each other 
(compare Section 28). 



THEORY OF THE POLARIZATION OF RESONANCE SPECTRA 



215 



100 



80 






40 



degree of polarization is the same for all members of a resonance 
progression; in the "classical" theory this has been taken for granted 
without a real proof. On the other hand, the degree of polarization can 
be widely different for two closely adjacent series, if they correspond 
to unequal values of /', and it can also differ for the two components 
of a rotational doublet. For the polarization, in general, is not the same 
for a given value of J' if the absorption or the emission process corre- 
sponds to lines lying on a P- or an i?-branch, or if both correspond to 
^-branch lines. Figure 79 shows 
the degree of polarization p as a 
function of /' for the five possible 
combinations of the two processes ; 
the branch designation in brackets 
[P], [<?], or [R] refers to the ex- 
citation process. The curves for 
R[P] and P[R] are almost coinci- 
dent, and it is noticeable that even 
for small values of J' all curves 
tend toward limiting degrees of po- 
larization, which are 50 % for Q [Q] 
and 14.3% for the others, thus 
agreeing exactly with the degree of 
polarization calculated for the clas- 
sical model of the rotating aniso- 
tropic oscillator. The points in Fi- 
gure 79 have been worked out by 
Mrozowski for the relatively simple case of a transition X TI -> 1 2, for 
instance, the one corresponding to the blue-green Na 2 -bands, where 
the ground state as a 27-state does not split up into several Zeeman 
levels. According to Placzek, however, the same calculations can be 
applied to transitions between all types of electronic states {1077). 

73. Experimental Results. The available quantitative experi- 
mental material suffices for testing all important predictions of the 
theory. The polarization has been determined separately for the two 
resonance spectra of Na 2 which are excited by the cadmium lines 
4800 and 5086A (marked by an asterisk in Table 31). The first of these 
series consists of singlets [Q[Q]), the other of doublets (P[R]). The 
measured polarization was p = 42 % for the singlets and p = 13 % 
for the doublets, in satisfactory agreement with the theory. Even 
better is the agreement obtained by Mrozowski for the resonance 
spectra which are excited by the Hg-line 4358A in selenium and 



To 




\ J^-\ 


5 6 PI 


V&^~~ 






4**M 


2 p[ 1L-~- 




"~6 7 P[P] 

1 



Fig. 79. Degree of polarization of 

the individual lines of a resonance 

spectrum. (Mrozowski). 



216 DIATOMIC GASES AND VAPORS 

tellurium vapor. He found p = 14.4 and 14.2%, respectively, arid, 
since these spectra belong to bands corresponding to 3 Z - 3 2J tran- 
sitions, Mrozowski's results prove the validity of Placzek's generali- 
zation of the originally restricted theory (1082, 12Q0). 

If a resonance spectrum is excited in the visible band system of 
iodine vapor by monochromatic light, p is the same for all members 
of the progression, and, in particular, Wood's i?-line, which coincides 
with the exciting line, is in no way distinguished with respect to the 
others. This result, which seemed somewhat surprising at first, must 
be expected according to the theory developed in the last section. 
Furthermore, Wood found the degree of polarization to be the same 
for the two components of a rotational doublet excited by the green 
mercury line. Although one component is an R[R] -line and the other 
an R[P]-line, there is no discrepancy with the theoretical values 
represented by Figure 79, since /' = 35 (see Table 25). If, however, 
the fluorescence is excited by circularly polarized light and is observed 
in the direction opposite to the primary beam, the polaiizations of the 
two doublet components differ. The "principal line" of the doublet for 
which /" = J" shows circular polarization of a degree only little below 
100% and of the same sense of rotation as the exciting line. The 
circular polarization of the "companion line"* for which /" =j" — 2 
is much smaller and the sense of rotation is ieversed. This effect was 
predicted theoretically by Placzek and has been actually observed by 
Daure and Kastler in the first positive doublet of the I 2 resonance 
progression excited by the green mercury line (260b, 1878). 

If the emission of the complete visible band system of I 2 is 
stimulated by the absorption of linearly polarized white light, the 
degree of polarization is about 13 % at room temperature and is not 
altered appreciably by doubling the absolute temperature at constant 
vapor pressure (127 5). \ Since these iodine bands consist only of P- and 
i?-branches, and since the average value of the rotational quantum 
number of the molecules at room temperature is of the order of 50 or 
more, p should be close to 14.3 % according to Figure 79. The 
agreement seems to be satisfactory. 

* Throughout this book J" and /" are used for the quantum number of 
the ground state before the absorption process and after the emission process, 
respectively. Thus, /* = /* is the R [i?]-component and J" = J" — 2 the 
R [0]-component. 

t The value of 18% given in earlier publications must undergo a correction 
because the multiple reflection in the compensating glass plates had been 
neglected. For the iodine fluorescence excited by the unresolved radiation of 
a hot mercury arc, Mrozowski obtained values of p between 15 and 20%. 



THEORY OF THE POLARIZATION OF RESONANCE SPECTRA 217 

When the fluorescence of iodine vapor is excited by plane-polar- 
ized light, the angular distribution of the fluorescence intensity shows 
a maximum in the direction perpendicular to the electric vector of the 
exciting radiation and a minimum in the direction parallel to this 
vector (421). 

The visible fluorescence bands of the alkali vapors Na 2 , K 2 , and 
Rb 2 exhibit considerably higher degrees of polarization. According to 
Dunoyer, the values of p are between 36 and 38 % in all three cases. 
These bands contain (^-branches as well as P- and i?-branches, and 
since all these branches overlap if they are excited by white light, the 
observed polarization represents an average value and can also be 
considered as a confirmation of the theory. Dunoyer assumed the 
existence of a connection between the degree of polarization of the 
fluorescence and the frequency of the molecular rotation, which is 
determined by the moment of inertia and the temperature. However, 
his conclusions were based on extrapolations which were certainly 
not correct. The apparent influence of temperature which he obser- 
ved was caused most probably by the simultaneous increase of 
vapor pressure and the depolarizing action of collisions (319). 

More extensive investigations of the influence of collisions on the 
polarization of the resonance fluorescence of diatomic molecules are 
available only for the visible bands of iodine. As may be expected, 
the depolarizing cross sections are, in contradistinction to the case of 
the atomic resonance radiation, relatively small; they are much 
smaller than the quenching cross sections. The depolarization is due 
mainly to collisions by which the spatial orientation of the molecular 
axis is altered, while a change of the rotational quantum number by 
one unit has a much weaker effect. "Transferring collisions" which 
affect only the vibrational energy produce no depolarization. In a 
fluorescence spectrum in which the primarily excited resonance pro- 
gression has been partially transformed by collisions into the band 
spectrum, the lines belonging to the new bands are actually less depola- 
rized than those for which v' has remained unchanged (ioj/j). The 
depolarizing efficiency of various foreign gases increases continuously 
with their molecular weight, from H 2 through He, N 2 , and Ne to A. 
If the fluorescence is quenched by the foreign gas, its depolarizing 
action is reduced because the lifetime of the excited state is shortened, 
exactly as in the case of monatomic vapors. Due to this circumstance 
and to the strong self-quenching of the iodine fluorescence, its polari- 
zation is practically independent of the iodine vapor pressure. The 
polarization of the iodine fluorescence is not appreciably altered by 



218 DIATOMIC GASES AND VAPORS 

external magnetic fields. If, however, the fluorescence has been 
partially depolarized by addition of helium at a few mm, the polari- 
zation is largely restored by applying a strong magnetic field, because 
the average lifetime of the excited state is shortened by "induced 
predissociation" (Section 66) (1079a). 

The ultraviolet Mc bands of iodine vapor differ essentially from 
the resonance bands' which have been treated so far, in that a tran- 
sition, probably without radiation, occurs between the absorption 
process and the final emission process. Since this transition is spon- 
taneous in the absence of collisions, the spatial orientation of the 
molecular axis remains unaffected and the rotational quantum number 
does not alter by more than unity. Thus, the polarization of the 
fluorescence should be practically unaffected by the transition. 
Actually, the polarization of the Mc bands is very considerable ; even 
with an addition of helium at 10 mm to the iodine vapor the bands 
still show a degree of polarization of 7 %, if the primary light is plane 
polarized, and a similar degree of polarization is observed in the band 
at 3460A which is strongly excited only by collisions with a foreign 
gas; the spatial orientation of the molecules is not completely de- 
stroyed by collisions which transfer them to another electronic state 
(1075). 



I. Sensitized Fluorescence of Diatomic Molecules 



74. Fluorescence Bands Excited in Hg-and Cd- Vapors on Addition 
of Foreign Gases. If excited mercury atoms are transferred to the 
metastable state by collisions with polar molecules like CO, the latter 
can re-emit the vibrational energy which they have taken up, as 
infrared radiation; this would be a typical case of sensitized fluo- 
rescence, but it would be almost impossible to observe an emission 
process of this kind. In genuine quenching processes, in which the 
excited mercury atoms Jose their total electronic energy in a collision 
with a diatomic molecule, the molecules are not raised into excited 
electronic states and thus excited to emit their own characteristic 
fluorescence; instead, the energy is consumed in producing a chemical 
reaction — for instance, a dissociation process — and only a small 
surplus of energy is available sometimes for an increase of vibrational 
or rotational energy of the newly formed molecules. If these molecules 
are sufficiently stable, however, they can undergo a second collision 



SENSITIZED FLUORESCENCE OF DIATOMIC MOLECULES 219 

with another excited atom and this may eventually stimulate the 
emission of sensitized fluorescence. 

As a matter of fact, the fluorescence spectraof mercury and cadmi- 
um vapor excited by the resonance lines of the metals contain in 
addition to the re-emitted resonance lines, bands of HgH,HgD,CdH, 
CdD, and, moreover, of OH and NH 3 , respectively, if hydrogen, 
deuterium, nitrogen, water vapor, or ammonia are present in the 
vessel. Whenever hydrogen participates in the reaction, its concentra- 
tion must be very low, because otherwise the strong quenching action 
of H 2 -molecules would destroy all excited mercury or cadmium atoms 
before any other sensitizing energy transfer could occur. These small 
amounts of hydrogen are then probably completely dissociated by the 
interaction with excited atoms. On the other hand, the presence of 
nitrogen or NH 3 increases the intensity of mercury-sensitized fluo- 
rescence in general, even if the nitrogen has no actual share in the 
reaction, because the lifetime of the excited atoms is increased by the 
transfer to the metastable state (47 1, 1034, igoi). 

The HgH-radicals are very unstable, as already mentioned in 
Section 40 ; they have practically no chance to survive more than one 
collision with an excited mercury atom. Therefore, the intensity of the 
HgH-bands (3100-4222A) is proportional to the square of the intensity 
of the exciting line ; two excited atoms are needed for every emission 
process. The CdH-molecules are comparatively stable; under constant 
illumination with the cadmium resonance line their concentration 
becomes so large that the intensity of CdH-bands (4198-4791A) in the 
fluorescence spectrum can be greatly enhanced by irradiating the 
resonance lamp simultaneously with the light emitted by an electric 
discharge through a mixture of hydrogen and of cadmium vapor. 
Under these conditions, the CdH-bands are produced not only as 
sensitized fluorescence but also by direct resonance excitation. This 
enhancing effect is obtained in analogous experiments with CdD and 
ZnH-vapors, but it is not observed with HgH and HgD-molecules. On 
the other hand, the CdH-bands appear under the same conditions of 
excitation when the atomic fluorescence of cadmium vapor is quenched 
by an admixture of propane vapor at a pressure between 1 and 7 mm 
(92,1173,1562). 

In the process of formation of the HgH-molecules by collisions of 
metastable Hg ( 3 P ) -atoms and H 2 -molecules, a surplus energy of 
0.62 eV is available, while there is an energy deficit of 0.1 eV 
if the hydrogen molecule is replaced in the process by a water mole- 
cule: 



220 DIATOMIC GASES AND VAPORS 

Hg <»P ) + H 2 -* HgH + H + 0.61 eV 
Hg ( 3 P ) + H 2 -> HgH + OH — 0.1 eVf 

Beutler and Rabinowitch assumed that the surplus energy of the first 
process is transferred partly into rotational energy of the HgH- 
molecule and that it is preserved as such until the excitation occurs by 
a collision with another Hg ( 3 P )-atom (106). This hypothesis has been 
proved to be erroneous by Rieke. Whatever their origin, the HgH- 
molecules attain the thermal equilibrium of their vibrational and 
rotational energy by collisions with N 2 or H 2 0-molecules. In the ensuing 
excitation process, vibrational and rotational energy is transferred to 
the HgH-molecules. Subsequently, the vibrational energy is con- 
verted almost completely into rotational energy by collisions with 
N 2 -molecules, while collisions with H 2 0-molecules are much less 
efficient, as pointed out in Section 67. Therefore, the HgH-bands show 
an abnormally high "rotational temperature" only when they are 
excited in the presence of nitrogen (1365a, 1365b). 

In addition to the HgH-bands, OH-bands, the so-called water 
bands, with edges at 2811 and 3064A, always appear in the mercury- 
sensitized fluorescence spectrum if water vapor is present in the vessel. 
Since excited mercury atoms are transferred with great probability to 
the metatable state by collisions with water molecules, the first 
process which occurs is, in general : 

Hg fPt) + H a O -> Hg (»P ) + H 2 + E, followed by. 
Hg ( 3 P ) + H 2° -* H § H + OH . and finally by: 
Hg ( 3 P ) + OH -> Hg (*S ) + OH* 

In the OH-band originating at the vibrational level v' = 0, the highest 
rotational quantum number observed is /' = 17, while in the band 
originating at the level v' = 1, J' reaches up to 12. These two levels 
of OH* (z/ = 0, J' = 17, and v' =1,7'= 12) lie immediately below 
the energy level of the mercury atom 6 3 P (963,964) . 

The intensity of the OH-bands increases more than propor- 
tionally to the first power, but less than proportionally to the 
second power of the primary light intensity. Therefore, it must be 
assumed that after the OH-radicals have been formed, some of them 
can be excited more than once before they are destroyed. The pro- 
cesses leading to the emission of the NH-bands, when H 2 and N 2 are 

f On the one hand, the dissociation energy of H 2 to H + OH is 118 kcal 
or 5.14 eV; on the other hand, the energy of formation of HgH is 0.37 eV and 
the energy of Hg (6 3 P ) is 4.7 eV (336). 



SENSITIZED FLUORESCENCE OF DIATOMIC MOLECULES 221 

added to the mercury vapor, must be still more complicated, since the 
dissociation of N 2 cannot be effectuated by a single collision with an 
excited mercury atom. Gaviola assumes metastable mercury atoms to 
be present in such great concentration, because of the interaction with 
nitrogen molecules, that three-body collisions between two metastable 
Hg-atoms and an N 2 -moIecule can occur and produce the dissociation 
of the latter. The heat of formation of NH from atomic hydrogen and 
nitrogen is supposed to provide the energy necessary for the excitation 
of the NH-bands. No special hypothesis has been proposed re- 
garding the excitation of the NH-bands by collisions of excited 
mercury atoms with NH 3 -molecules. Whatever the mechanism of their 
production may be, the NH-radicals are also relatively long-lived, 
since the intensity of the NH-bands follows nearly the same law as 
that of the OH-bands in its relation to the energy of the exciting 
radiation. In the presence of N 2 , the red and violet CN-bands are 
frequently observed in the mercury-sensitized fluorescence. The carbon 
atoms are probably produced by dissociation of some organic stopcock- 
grease vapor. The phenomenon has never been investigated any 
further. 

All bands mentioned in the last paragraphs show fine structure 
and can be ascribed unequivocally to their carriers. The origin of two 
additional continuous bands has not yet been explained satisfactorily. 
The first, between 2900 and 4000A, occurs only in the presence of 
NH 3 and the other, between 2537 and 3200A, in the presence of H 2 0- 
vapor. They are produced by a single absorption process, since, in this 
case only, the intensity of the fluorescence is directly proportional to 
the intensity of the incident mercury resonance line. Wood and 
Gaviola suggest that a complex molecule of high energy is formed by a 
collision of an excited mercury atom and an NH 3 or H 2 0-molecule, 
respectively, and that the emission of the bands is caused by the 
disintegration of these complexes (4ji,tgoi). 

The Hgl-bands at 4525A (compare Sections 65 and 93) form a 
part of the fluorescence spectrum which is emitted if a mixture of I 2 - 
vapor and nitrogen containing traces of mercury vapor is irradiated 
with the mercury resonance line at a temperature of 800° C. The bands 
disappear from the fluorescence if the exciting mercury line is self- 
reversed; the radiation by which they are excited is thus absorbed 
primarily by normal mercury atoms. The emission of the bands may 
be due either to the formation of excited Hgl-molecules by collisions 
of excited iodine molecules with excited mercury atoms, or to the 
sensitized fluorescence of Hgl-molecules present in the vapor (333). 



222 



DIATOMIC GASES AND VAPORS 



If a mixture of iodine vapor and nitrogen is illuminated at room 
temperature with short-wavelength u.v., a deep green fluorescence is 
observed. It is caused by the emission of a band having a width of 
about 200A and showing some fine structure. It cannot be obtained in 
pure iodine vapor nor in pure nitrogen, not even by an electric 
discharge, nor does it appear in iodine vapor if any other gas is added 
instead of nitrogen. The band begins to be noticeable at a nitrogen 
pressure of a few cm and its intensity increases continuously if the 




Hg(6 'P,) 



Hg (6 V>„) 



Fig. 80. Potential curves for the system rare gas-mercury (Oldenberg). 

a: first short-wavelength max. c, d: long-wavelength bands. 

b; second short- wavelength max. e: atomic line. 



nitrogen pressure is raised to one atmosphere and more. Apparently 
the iodine molecules are able, in their highly excited state, to form 
iodine-nitrogen compounds of great energy which emit the green band. 
Such processes, including some of those mentioned in the preceding 
paragraphs, are perhaps better designated' not as sensitized fluorescence 
but as photo-chemiluminescence : the energy of the primarily excited 
molecules induces a chemical reaction which, in turn, causes the 
emission of light (360,1161). 

75. Rare Gas-Mercury Bands. Unexcited mercury atoms are not 
able to form stable molecules with the atoms of helium or other rare 
gases; if the mercury atoms are in the excited state & S P 1 or 6 3 P , 
however, such molecules can exist, though their heats of dissociation 



RARE GAS-MERCURY BANDS 223 

are very low. Figure 80 shows the potential curves for the systems rare 
gas-Hg (S^o) and rare gas-Hg( 3 P a ). Two states of repulsion, which 
also occur in the second case, can be disregarded in this connection ; 
the minima of the attraction curves are very shallow. The distance 
between the dotted horizontal line and the horizontal branches of the 
attraction curves corresponds to the average thermal energy of the 
atoms at room temperature. The points at which the dotted line 
intersects the potential curves determine, therefore, the distance to 
which, on the average, the two atoms approach each other, or the 
most probable turning points: they are located on both curves 
above the dissociation level of the loosely bound molecules and 
correspond to nonquantized states. Transitions from there to the 
potential curve N of the ground state cause the emission of two broad 
lines which are displaced in the direction of shorter wavelengths with 
regard to the normal mercury resonance line, as already mentioned 
in Section 36. 

If, however, the excited mercury atom and the atom of the rare 
gas approach each other with low velocities, weakly bound mer- 
cury-rare gas molecules can be formed in three-body collisions. 
Because of the shallowness of the potential trough, the number of 
rather closely spaced vibrational levels of these molecules is small. By 
transitions from these levels to the almost horizontal potential curve N 
of the ground state, the molecules dissociate and, simultaneously, 
emit fluorescence bands which show fluctuations almost exactly 
reproducing the structure of the vibrational levels of the excited 
molecules. 

Oldenberg observed the fluorescence excited at room temperature 
by the nonreversed Hg resonance line in mercury vapor to which rare 
gases (He, Ne, A, Kr, and Xe) of pressures up to one atmosphere were 
added, so that three-body collisions had a sufficient probability. In 
addition to the two "collision lines" on the short-wavelength side 
of the resonance line, which have been mentioned above, Oldenberg, 
in these experiments, obtained the emission of bands on the long- 
wavelength side of the resonance line. They appeared to be continuous 
in the case of helium and xenon and showed only traces of fluctuations 
with neon, but with argon and krypton they were resolved into a 
series of maxima converging in the direction of greater wavelengths : 
a first sequence of maxima stretches from 2541.7 to 2549A, and from 
2541.1 to 2548.5A, respectively, and in both cases weaker and more 
closely spaced bands follow, reaching to 2554A for argon and to 2557A 
for krypton. At high mercury pressures these bands are also obtained 



224 DIATOMIC GASES AND VAPORS 

in the absorption spectra of the mixed vapors, but under conditions 
prevailing in Oldenberg's fluorescence experiments the mercury vapor 
pressure was low and the light absorption could occur only in normal 
mercury atoms (#49, 1166,1169). 



J. Luminescence of Diatomic Metal Molecules That Are 
Stable Only in Excited States 

76. Fluorescence Bands of Hg 2 . The emission of various fluo- 
rescence bands by pure mercury vapor has been known for a long time 
and has been the subject of a large number of publications ; the most 
important of these are due to the younger Lord Rayleigh. Similar 
fluorescence bands have been observed in the vapors of cadmium and 
zinc and in mixtures of these vapors. Contrary to the processes dealt 
with in the preceding sections, the bands which are under consider- 
ation here are, in general, not produced by absorption of the resonance 
line of the metal but by irradiation of the vapor with light belonging to 
other spectral regions. Furthermore, some of the bands occur in the 
absorption spectrum under the same experimental conditions under 
which the fluorescence is obtained. 

Table 44 shows spectral location, type, and occurrence or non- 
occurrence in the absorption spectrum for all fluorescence bands which 
have been observed in Hg-vapbr. An almost complete interpretation 
of their production and their complicated dependence on temperature 
and pressure has become possible on the basis of the potential-curve 
diagram reproduced in Figure 81.* The "dissociation products" in the 
second row of Table 44 can also be derived from the diagram (841, 
897(1,1065,1068,1073, 1345-1348,1735) . 

Aside from the weak polarization forces which cause a very shallow 
minimum at a relatively large internuclear distance in the potential 
curve, only repulsive forces exist between two unexcited mercury 
atoms. The heat of dissociation of the "van der Waals molecules" 
bound by the polarization forces is of the order of only 0.06 eV and 
these molecules are, therefore, very unstable even at room tempera- 
ture (798,1066). However, at the relatively high vapor pressures 

* Bands which have been observed only in the absorption spectrum and do 
not seem to be related to the excitation of fluorescence are not mentioned in the 
table, but some of them are indicated in Figure 81. Concerning the designations 
used in the figure and their theoretical foundation, the original papers by 
Mrozowski and others must be consulted. 



FLUORESCENCE BANDS OF Hg 2 



225 



between several mm and one atmosphere at which the fluorescence 
bands are observed, the actual distance between many atoms is not 



70 



60 



50 



40 



30 



20 



10 




eo ro ro — "* 

* KIN 

$ E 







6 'S 



Fig. 81. Potential curves of Hg 2 (Mrozowski). 



greater, or is even smaller, than the internuclear distance in the van 
der Waals molecules. On the other hand, mercury atoms in the excited 
states 6 s P ,i,2, 61 ^i. ? 3 Si, etc., are able to form stable genuine mole- 
cules with unexcited mercury atoms. The heat of dissociation of these 



226 DIATOMIC GASES AND VAPORS 

molecules in some cases exceeds 1 eV, and their vibrational and 
rotational energies are completely quantized. If the distance between 
two unexcited atoms is sufficiently small, they can be raised by ab- 
sorption of light, in accordance with the F.C. principle, to one of the 
potential curves representing a stable molecular state, from which 
the emission of fluorescence subsequently originates. 

The mercury bands listed in Table 44 can be divided into three 
groups : (j) the narrow bands (e),f, and g at (3650),* 2540, and 2345A, 
repectively ; they are closely connected with the electronic transitions 
in the normal atoms and are ascribed to transitions between van der 
Waals molecules in the ground state and in higher electronics states. 
(2) Long sequences of typical fluctuations (bands c, d, and h) which 
can correspond only to transitions from excited molecular states to the 
nearly horizontal branch of the lower potential curve N. Even when 
excited with monochromatic light of different wavelengths, in general 
the whole sequence of fluctuations is emitted, because the same average 
distribution over the various vibrational levels of the excited state is 
produced by collisions. (3) Broad bands without any structure which 
probably also originate from excited stable molecules, but which 
correspond to transitions onto a part of the lower potential curve 
where its slope is already relatively steep. At moderate temperatures 
and vapor pressures these bands (and also band h) are missing in the 
absorption spectrum, because the relative thermal energies of the 
unexcited atoms are practically never so large that they can approach 
each other sufficiently closely (see Figure 81). However, in mercury 
vapor of high pressure (about one atmosphere) , light of all wavelengths 
between 3750A and the far u.v. is completely absorbed and it is not 
possible to decide how much the individual processes contribute to the 
total absorption. 

Since the possible transitions are very numerous and the energy 
differences between the individual potential curves are small, ab- 
sorption bands caused by transitions between the ground state and 
various excited states will frequently overlap, so that two emission 
processes can be excited by primary light of one wavelength. If two 
such absorption processes originate from different parts of the po- 
tential curve N, the corresponding emission bands may show an 
unequal dependence on temperature and vapor pressure. On the other 
hand, an emission process may not originate at all from the directly 
excited electronic state, because the molecule is transferred into 

* This so-called band at 3650A is, according to Mrozowski's latest publi- 
cation, not a separate band but rather the short-wavelength edge of band c or d. 



PROPERTIES OF THE INDIVIDUAL Hgg-BANDS 



227 



another potential curve before the emission occurs. If this is a repulsion 
curve, the molecules dissociate into atoms, some of them being in the 
metastable states 6 3 P 2 or 6 3 P ; these can later recombine with other 
atoms to from some sort of excited molecules. Finally, the formation 
of such molecules can also follow the primary production of excited 
atoms by the absorption of the resonance line. 

Table 44 
Fluorescence Bands of Mercury Vapor 



Band designation 


a 


6 


c 


d 


t 


f 


e 


h 


i 


Products of 
dissociation 


6 3 P„ 


6 3 P 1 


e 3 P 1 


&P X 


? 


&P 1 


&>P 2 


&P X 


&P X 


Wavelengths 
of band (A) 


5500- 
3500* 


3950- 
3020f 


3020- 
2760 


2930- 
2760 


2650 


2540 


2345 


2345- 
2100 


2000- 
1810 


Type of band 


cont§ 


cont 


fl" 


fl 


nar- 
row 


nar- 
rowi# 


nar- 
row 


fl 


cont 


Occurs in 
absorption 


— 


— 


— 


+ 


+ 


+ 


+ 


+ 


+ 


Corresponding 
atomic line 


2656 


2537 


2537 


2537 


2270 


2537 


2270 


1849 


1849 


Excitation 
bands 


i, h, d, 
to 3450 


C, W 
to 3360 


C** 


W** 


f,c 


f.c 


i,C 


i, h 


i 



* Maximum at 4850. t Maximum at 3380. =j See footnote, page 226. § cont 
= continuous. " fl = fluctuation bands, ii Possibly with some structure. 
** C and W = "core and wing excitation," according to Lord Rayieigh's 
nomenclature (see Section 77). 

77. Some Properties of the Individual Hg 2 - Bands. The band 
designations in the first row of Table 44 correspond to those used in 
Figure 82. The last row shows that most of the fluorescence bands can 
be excited by light absorption in more than one of the absorption 
bands. It seems almost certain for instance, that at least four primary 
processes must be considered for the excitation of band a, with a 
maximum of intensity at 4850A. The band is excited at a vapor 
pressure of 600 mm (320° C) by light of wavelengths up to 3200A and 
at pressures above one atmosphere, even by light of 3450A. It cannot 
be ascertained which of the' original excitation regions has spread so 
far under these conditions. C and W, which are also mentioned in 
Table 44 as extiting band a, stand for Lord Rayleigh's "core" and 



228 



DIATOMIC GASES AND VAPORS 



"wing" excitation, respectively. The former is used for excitation by 
the almost nonreversed "core" of the Hg resonance line, while the 
latter designates excitation by the strongly self-reversed resonance 
line or by lines adjoining this line in the direction of greater wave- 
lengths (1348). 

The excitation spectrum of the continuum b, with maximum at 
3380A, coincides very closely with that of band a. However, according 
to Rayleigh, the relative intensities of a and b depend very much on 
the vapor pressure and the temperature. With wing excitation, as 



Hg 



Cd 



Zn 




5000 4500 3900 3261 3078 2500 

3 P 
OJ,Z 



2289 2114 
>P 



TTT 



A(?) 



4900 4000 3075 2400 2138 

— ""» Fluctuations -continuous bands 

Fig. 82. The fluorescence bands of Hg 2 , Cd 2 , and 2n 2 (Mrozowski). 



well as with core excitation, the green band a prevails at pressures 
above 20 mm; at pressures below 5 mm the u.v. band b is the stronger 
one. Since neither occurs in the absorption spectrum at these pressures, 
the change in relative intensities cannot be due to reabsorption. On 
overheating the vapor at a constant pressure of 60 mm, the intensity 
of band b increases steadily, while band a vanishes completely. 
Mrozowski explains this behavior by assuming that an increase of the 
number of collisions between Hg-molecules, due to higher temperature 
or higher pressure, increases the probability of a transfer from the long- 
lived metastable state ^4 3 0„ to the state A 3 l u and thus favors the 
emission of band b in comparison with a. 

The emission of the narrow band g is not only caused by excitation 
with light of A <--• 1850A, but also by core excitation ; in the latter case, 
g is followed by a further number of narrow bands at 2338, 2334, and 
2330A which overlap band h but apparently do not belong to this 
system. 



PROPERTIES OF THE INDIVIDUAL Hg 2 -BANDS 229 

The fluctuation band h itself (2345 to 2100A)* overlaps a series 
of similar absorption bands reaching from 1849 to about 2260A and 
corresponding to the same electronic transition. The light ab- 
sorption in these bands excites the emission of band h, which consists 
of a long sequence of maxima and minima. The spacing of the fluctu- 
ations is about 600 cm -1 near the band head at 2300A, but decreases 
to 150 cm" 1 at 2100A. The intensity distribution within the band and 
the exact location of the individual maxima depend on the wavelength 
of the primary light : the shorter the latter, the farther the emission 
band stretches in the direction of greater wavelengths. f In this 
respect, the Steubing bands differ from all other Hg fluorescence 
bands. According to Mrozowski, this is due to the fact that the various 
levels from which the individual fluctuation maxima originate corre- 
spond to different rotational quantum numbers and not to different 
values of v' . The J's are much less affected by collisions than the v's. 
As shown in Figure 81, the wavelength of the light absorbed in band h 
is the greater, the smaller the interatomic distance at the moment of 
absorption, or the greater the relative energy of the two atoms before 
the collision. Therefore, the average angular momentum with respect 
to the common center of gravity and the ensuing rotational energy of 
excited molecule are the larger, the greater the wavelength of the 
exciting light {ioy 3,1572). 

The band i adjacent to the singlet resonance line 1849A (6 1 P 1 - 
VSo) is excited by light of wavelengths below 2000A. If the primary 
radiation consists of monochromatic lines — for instance, the alumi- 
num lines 1854, 1882, 1935, and 1990A — these lines themselves 
appear with great intensity, superimposed on the continuous band 
in the fluorescence spectrum: The same phenomenon was first ob- 
served by Kapuscinski in the fluorescence of cadmium vapor and is 
treated in more detail in Section 81. 

The two fluctiation bands c and d originally were called wing and 
core bands by Lord Rayleigh because he obtained the one by wing, the 
other by core excitation (1347). Both consist of long series of fluctu- 
ations with a spacing which decreases towards smaller wavelengths ; in 
band c the distance between adjoining maxima is about 160 cm -1 at 
2900A and about 100 cm- 1 at 2780A. In spite of the differences in 

* The fluorescence band h and the correlated absorption band was first 
observed by Steubing and is, therefore, frequently called the "Steubing band." 

t The narrow band g, which is also strongly excited by light of wavelengths 
below 2000A, remains unaffected by these changes and is thus proved to be 
independent of the band system h. 



230 DIATOMIC GASES AND VAPORS 

location and spacing observed by Rayleigh in the two bands, they are 
so similar that it seems plausible to ascribe them to the same electronic 
transition. On the average, the spacing is slightly larger in band c, 
but also less regular, so that it may rather correspond to a super- 
position of several series. It is not improbable that c and d differ only 
by the amount of rotational energy which has been imparted to the 
molecules in the process of formation. This might be the reason why 
only one of them (d) is observed also in the absorption spectrum of the 
vapor. On the other hand, band c can be excited by an electric dis- 
charge through mercury vapor. 

All processes of excitation listed in Table 42 lead directly to the 
formation of diatomic mercury molecules, with the sole exception, 
perhaps, of "core excitation," which Lord Rayleigh is inclined to 
ascribe to absorption by unperturbed normal Hg-atoms. However, 
experiments which will be described in Section 81 make it more 
probable that this so-called core absorption takes place in van der 
Waals molecules (io68,njy,i2g6). 

The intensity of all mercury absorption bands of greater wave- 
lengths increases with the square of the vapor pressure, in agreement 
with the assumption that two atoms participate in every absorption 
process. (Some deviations from this law have been reported by 
Mrozowski). 

78. Lifetime of the Bands and Their Sensitivity to Collisions. The 
band fluorescence of mercury vapor is characterized by a distinctive 
property: some of the bands exhibit a very appreciable afterglow. 
From the point where the luminescence is excited, it is carried along 
by streaming mercury vapor over relatively large distances. Phillips 
was the first to observe the phenomenon, which has since been investi- 
gated frequently. In Phillips' experimental arrangement, the length 
of the luminous column was 50 cm; the rate of flow could be de- 
termined from the temperature gradient along the tube and, thus, 
the duration of the afterglow was calculated to be about 10 sec {1231). 
The afterglow can be produced by wing and core excitation and by 
irradiation of the vapor with the short-wavelength u.v. from an 
aluminum spark. The emission spectrum consists mainly of the bands 
a and b and the narrow band /; the other bands have never been 
mentioned in this connection. Lifetimes of that order can be explained 
only by assuming that metastable systems participate in the process : 
either the excited molecules themselves are partially in metastable 
states, as may be expected for configurations derived from atoms in 
the states 6 3 P and 6 3 P 2 , or metastable atoms are produced by the 



LIFETIME OF Hg 2 -BANDS AND SENSITIVITY TO COLLISIONS 231 

intermediate reactions which occur in most of the excitation processes. 
The production of metastable Hg-atoms at the point where band 
fluorescence is excited by the absorption of light of wavelength 2540A 
(band f) has been proved by Rayleigh; under these conditions of 
excitation, it was possible to obtain the emission of the higher atomic 
series lines by "stepwise excitation" and, furthermore, the emission 
of the "forbidden lines" 2656A (6 3 P -> 6^ and 2270A (6 3 P 2 -> 6^0) . 
This is the only instance in which the second of these lines has ever 
been observed in fluorescence ; even in this case its intensity was very 
weak. If the band fluorescence is excited by light of wavelength 
2850A (band d), no metastable atoms are found in the vapor [1346a, 

1347)- 

On the other hand, the atomic resonance line 2537A occurs 
wherever the band fluorescence is excited by light of wavelengths 
< 2537A, and even as anti-Stokes fluorescence, if the primary ra- 
diation corresponds to the band/ (2540A)*, but not on excitation by 
light of still greater wavelengths. If the band fluorescence is excited by 
the light from an aluminum spark, the resonance line is "carried 
along" by the vapor as far as the green band a; with core excitation 
this occurs only at low pressure (about 2 mm) and over relatively short 
distances. However, under these conditions the spectrum of the after- 
glow contains several other atomic lines of low intensity originating 
from higher electronic states (e.g., 7 3 £> 2 and 7 1 5 , compare Figure 15) ; 
these lines could not be excited "stepwise" by light absorption, but 
only by collisions, since the corresponding lines were not present in the 
spectrum of the primary radiation. If mercury vapor at atmospheric 
pressure is irradiated with the light from an aluminum spark, the 
visible mercury triplet is also emitted in addition to the bands g and 

/ (1348). 

Wood made the observation that a dark space occasionally 
seemed to intervene in a mercury-vapor jet between the point of 
excitation and the beginning of the visible afterglow {1884). According 
to Rayleigh, who investigated this phenomenon extensively, the dark 
space is most pronounced if the fluorescence is excited by light of 
wavelengths below 2000A; it is less obvious with wing excitation and 
completely absent with core excitation. A similar dark interval has 
never been found in the emission of the continuum b and the. other 
bands listed in Table 44. Both duration of the afterglow and the ex- 
istence of the dark interval have been ascertained by Wood by 

* The resonance line is missing at higher vapor pressures because of 
reabsorption, if the fluorescence originates from the interior of the vapor. 



232 DIATOMIC GASES AND VAPORS 

phosphoroscopic methods. A slow increase of the fluorescence intensity 
after the irradiation period can be understood if the excited state is not 
reached directly by the excitation process and if at least one of the 
intermediate states into which the molecule is transferred after the 
absorption of light is metastable. Under these circumstances, the 
conditions (as Kapuscinski has pointed out) are analogous to the 
production of a radioactive element from a parent substance, if several 
intermediate elements of not too short lifetimes are formed in the 
process. If some of the intermediate states are sufficiently long lived, 
the initial growth of the final product can be so slow that a genuine 
dark interval may seem to exist. The actual occurence of a perfectly 
"dark" interval can hardly be explained on the basis of any theory 
{716,1233,1348). 

It has already been mentioned that for most of the mechanisms 
under consideration, several collision processes must intervene between 
the absorption and the emission of light. Relatively large deviations 
from Stokes' law are not infrequent, as, for instance, the core exci- 
tation of band g (energy deficit AE = 0.4 eV), the excitation of the 
complete band b (3950-3020A) by light of A = 3450A (AE < 0.3 eV), 
and the core excitation of the higher atomic lines. The thermal energy 
is not sufficient to supply these "deficiencies" and it must be assumed 
that two or more primarily excited molecules or atoms partake in the 
collision processes. 

The sensitivity of the fluorescence bands to quenching or en- 
hancing collisions, particularly with hydrogen or nitrogen molecules, 
is closely connected with the lifetimes of the excited states. The 
influence of collisions is very weak for the bands near 1849A, which do 
not occur in the afterglow and probably have a very short lifetime. 
The other short-wavelength band h is also little affected by the ad- 
dition of foreign gases; nitrogen has a rather greater quenching effi- 
ciency than other gases, while the fluctuations retain their normal 
structure and intensity distribution. On the other hand, the bands 
g and / are considerably weakened by the presence of hydrogen, the 
H 2 half-value pressure being about 25 mm. On addition of nitrogen, 
the band g disappears completely and simultaneously the green band a 
is greatly enhanced. Probably both phenomena are caused by the well- 
known transfer of mercury atoms from the state & 3 P 1 into 6 3 P by 
collisions with nitrogen molecules.* Even in mercury vapor saturated 

* If it is correct that the intensity of the band b is also increased to some 
extent by addition of N s , it must be explained by secondary transitions from 
^ 3 0,,into AH U . 



LIFETIME OF Hg 2 -BANDS AND SENSITIVITY TO COLLISIONS 233 

at room temperature (p = 10 -3 mm) to which nitrogen of atmospheric 
pressure has been added, the emission of the visible fluorescence band 
is excited by irradiation with the resonance line with considerable 
intensity. Under these conditions, the only possible process is the 
transfer of the excited 6 3 P 1 -atoms into the metastable state and sub- 
sequently, probably in a three-body collision, the combination of the 
metastable atom with another mercury atom to form excited Hg 2 - 
molecule. It is plausible to assume that analogous processes occur 
also in mercury vapor of high pressure in the absence of nitrogen 

[1073,1347)- 

The green fluorescence band is exceedingly sensitive-to quenching 
by hydrogen; according to Pringsheim and Terenin, it is completely 
destroyed by hydrogen at a few thousandths of a millimeter. This 
observation provided the explanation of a phenomenon which, for a 
time, was the source of rather strange speculations. In certains ex- 
periments the green band failed to appear in the fluorescence spectrum 
of stagnant mercury vapor, while it reappeared as soon as a tempera- 
ture gradient which caused the mercury to distill from one end of 
the tube to the other was established in the observation chamber. 
Apparently, traces of H 2 were present and were "pumped" by the dis- 
tilling vapor to the cooler end of the tube. Wood and Voss also 
eventually interpreted their puzzling results by this assumption. 
According to Winans, the same interpretation cannot be applied, 
however, to a similar phenomenon observed in a mixture of mercury 
and zinc vapors, which will be mentioned in the last paragraph of 
Section 80 (1299,1847,1914). 

Lord Rayleigh confirmed Pringsheim's and Terenin's results in 
the case of "core excitation'' of the green band, while he found the 
visible fluorescence to be not noticeably weakened even at hydrogen 
pressures of several mm when "wing excitation" was used. This 
discrepancy has not yet been cleared up in a satisfactory manner. 
According to Section 38 a strong quenching by hydrogen should always 
be expected if metastable systems of an electronic energy near 4.5 eV 
are formed in the process of excitation. It is not surprising, therefore, 
that the green fluorescence is not quenched by hydrogen when it is 
excited by absorption of light in the band d or even by light of 
A > 3000A {1299,1347). 

The long-wavelength bands a and b which are distinguished by 
their long lasting afterglow, and apparently, also, the fluctuation bands 
c and d, are always completely depolarized, even if they are excited by 
plane-polarized light. If the molecules are formed by the combination 



234 DIATOMIC GASES AND VAPORS 

of an excited and an unexcited atom, it is impossible that any pre- 
ferential orientation of the primary electronic oscillator survives this 
process. Long life of the excited states is, of course, also apt to destroy 
an originally existing polarization. On the other hand, the fluctuation 
band h and the narrow band / are partially polarized if excited by 
absorption of short-wavelength u.v. (A < 2000A). If the fluorescence is 
observed in the direction perpendicular to the unpolarized primary 
radiation, the degree of polarization p„ of either band is about 5 %, 
corresponding to p p = 9.6 %. The molecules emitting these bands are 
formed directly in the absorption process, and, since they are relatively 
short lived, they undergo only a small number of collisions during their 
lifetime. As stated in Section 73, the orientation of the molecular axes, 
which is determined by the absorption process, is not completely 
destroyed by a moderate number of collisions (1077,1082,1930). 

The polarization and intensity of the Hg 2 fluorescence bands is 
not appreciably influenced by magnetic fields. An apparent weakening 
of the green band, when it is excited by the mercury resonance line, 
is, according to Mrozowski, a secondary effect; it is caused by the 
"magnetic filtering" of the primary radiation by the vapor layer 
adjacent to the walls of the vessel (see Section 9) (1080). 

79. Sensitized Fluorescence Induced by Hg 2 -MolecuIes. It has been 
pointed out in Section 40 that, if sensitized fluorescence is excited in 
mercury vapor of high pressure, Hg 2 -molecules may play a part in the 
process. This has been proved with certainty by Mrozowski: he 
irradiated a mixture of mercury and thallium vapor with lines from 
aluminum or zinc sparks, which are not absorbed by mercury or 
thallium atoms, but only by Hg 2 -molecules. At temperatures above 
275° C, he obtained the two thallium lines 5350 and 3776A in the 
fluorescence spectrum; the intensity of the lines increased continu- 
ously with increasing temperature up to 800° C, and additional lines 
originating from higher excited states of thallium appeared at the 
same time. This is caused only to a small degree by the higher thermal 
energy available ; in the main, it is due to the greater density of the 
thallium vapor, which enhances the probability of collisions between 
thallium atoms and Hg 2 -molecules in highly excited states before these 
lose a part of their energy by collisions with other Hg 2 -molecules or 
Hg-atoms. 

Under these conditions, the relative intensities of the various 
thallium lines are widely different from the intensity distribution in 
the sensitized thallium fluorescence excited by the mercury resonance 
line in mercury vapor of low pressure. The difference is explained by 



FLUORESCENCE BANDS OF Cd 2 , ETC. 235 

the absence of the "energy resonance" which is known to play an 
important part in the energy transfer from Hg (6 Z P-,} -atoms to other 
metal atoms (compare Section 40). 

The fluorescence emission of the Hg 2 -bands themselves is also 
affected to a certain degree by the presence of thallium vapor. In con- 
trast to the results obtained in pure mercury vapor, the green band a 
remains stronger than the u.v. band b at temperatures up to 500° C, 
even if the vapor is overheated. Probably the Hg 2 -moIecules in high 
vibrational levels of the state A z %, which in the absence of thallium 
atoms would be transferred by collisions into the state A 3 1„ (origin of 
band b), transmit their energy with greater efficiency to thallium 
atoms because of energy resonance with the thallium term 7 3 S 1/2 . 
The band a vanishes and is replaced by a narrow band at 4550A only 
if the temperature is raised above 500° C. The origin of this band is 
uncertain; it should perhaps be ascribed to a HgTl-molecule. (Con- 
cerning the occurence of HgTl-bands, see next section). In Mrozowski's 
experiments the spectrum of the sensitized fluorescence also contained 
the cadmium line 3261 A; apparently the thallium sample was con- 
taminated with traces of cadmium (ioygb). 

80. Fluorescence Bands of Cd 2 , Zn 2 , and ot Mixtures of Various 
Metal Vapors. After the detailed treatment of the band fluorescence of 
Hg 2 - vapor, similar phenomena in the vapors of cadmium and zinc can 
be dealt with more briefly, inasmuch as the experimental data are 
much scantier-; most of them are due to Jablonski, Kapuscinski, and 
their collaborators. 

The potential curves for Cda and Zn 2 can be assumed to be 
essentially the same as those of Hg 2 reproduced in Figure 81 . The bands 
which have been observed are drawn schematically for the three 
vapors in Figure 82, after a representation given by Mrozowski. As 
far as possible, the designations of the bands correspond to those used 
for Hg 2 in Table 44 and in Figure 81. The absorption bands of the 
vapors again coincide, in general, with the bands in the fluorescence 
spectra, but again the long-wavelength bands which extend partially 
into the visible region are missing in the absorption spectrum (b and 
c in Figure 82) (242,244,657 ,710,712 ,715,717 ,1070,1076,1262 ,1601 , 

1734)- 

The structure of the Cdj-band h (2627-3050A) depends on the 
wavelength of the incident light, as in the case of the analogous Hg 2 - 
band h; furthermore, the location of the individual fluctuation maxima 
is strongly influenced by the temperature. The spacing of the maxima 
corresponds to 460 cm -1 - at the long-wavelength end of the band and 



236 DIATOMIC GASES AND VAPORS 

decreases to 80 cm -1 at the short-wavelength end. In the overlapping 
region between 2640 and 2820A, the maxima in the fluorescence 
spectrum coincide almost exactly with the fluctuations in the ab- 
sorption spectrum. 

If the fluorescence is excited by the strong magnesium-line group 
between 2803 and 2936A, the short-wave part of the emission band is 
missing and the fluorescence spectrum consists only of seven fluctu- 
ation maxima between 2800 and 3000A. If, on the other hand, the 
fluorescence is excited by monochromatic lines of the spectral region, 
where the absorption and the emission bands overlap, the fluorescence 
spectrum shows a very pronounced and narrow maximum of intensity 
at the wavelength of the exciting line, almost as in a resonance re- 
emission. Under these conditions, the fluctuations are restricted to the 
"Stokes part" of the band h, while the "anti- Stokes part" is continu- 
ous and does not reach far beyond the exciting line (715). 

The fluorescence of the Cd 2 -band k, which has no known analogue 
in the Hg 2 -spectrum, can be excited only by light of A _< 2114A. In 
the fluctuation bands c and d, which were obtained by irradiating the 
vapor with the light from a Cd-spark, the wavelengths of thirty-three 
maxima were measured by Kotecki in the spectral region between 
4290 and 2633A with a spacing decreasing from 236 to 81 cm -1 . 
Irradiation with light of wavelengths below 2290A causes the emission 
of the visible band b. Kapuscinski proved, by means of a rotating 
mirror phosphoroscope, that this band shows an afterglow of about 
10~ 4 sec and a period of growth <~ 10~ 5 sec. In this respect, the band 
is analogous rather to band a than to band b of Hg 2 . The lifetime of 
the other Cd 2 -bands is very much shorter (714,716,812,813). 

The fluorescence bands of Zn 2 are less easily observed; their 
intensity is always low and they are very sensitive to small traces of 
impurities. Their spectral location is shown in Figure 82. In the short- 
wavelength part between 2456 and 3073A, twenty-three fluctuation 
maxima could be identified ; the intervals between them decrease (at 
an even greater rate than in the other vapors) from 700 cm" -1 at 3000A 
to 200 cm -1 at 2450A. The phenomenon of "line re-emission" has 
been observed also in these bands. 

The similarity between the Hg 2 -bands on one side and the Cd 2 
and Zn 2 -bands on the other, also prevails with regard to their polari- 
zation. The visible Cd 2 and Zn 2 -bands are always unpolarized. The 
degree of polarization of the band h of Cd 2 is 5.5 %, if the fluorescence 
is excited by unpolarized light, and 1 1 % if the primary radiation is 
plane polarized. The polarization is very little influenced by the vapor 



FLUORESCENCE BANDS OF Cd 2 , ETC. 237 

pressure. In consideration of a question occurring in the next section, 
it is important that the "re-emitted lines" in the Cd 2 -band h are 
polarized to exactly the same degree as the underlying fluctuations. 
The degree of polarization of the Zn 2 -band h is even supposed to be 
appreciably higher (14.5 %) than in the other instances, but this result 
may be due to errors in the rather difficult measurements (1158,1,541). 

If the fluorescence of cadmium and zinc vapor is excited by short- 
wave u.v. at sufficiently great vapor densities, the spectra contain a 
considerable number of atomic lines in addition to the molecular 
bands, some of them originating from higher excited levels. Stepwise 
excitation is out of the question also in this case if the primary 
radiation is produced by sparks between iron or aluminum electrodes. 
The intensities of some of the lines, e.g., the triplet 5 3 D 2 -> 5 3 P 0t 1( 2 of 
Cd, or the triplets 4 3 Z> 2 -» 4 3 P 0> x> 2 and 5 3 S 1 -> 4 3 P 0) h 2 of Zn, are pro- 
portional to the square of the intensity of the primary light, while the 
intensity of the resonance lines of Cd and Zn, respectively, and that 
of some of the other lines is proportional to the primary intensity 
itself. The contribution of two excited molecules is needed for the 
production of the high atomic excitation states, while one excited 
molecule, in addition to the available thermal energy, suffices for 
exciting the lower states ; when this is no longer the case at decreasing 
temperatures, the ratio between the primary and the secondary in- 
tensities, instead of being linear, tends to become quadratic even for 
the resonance lines (1842). 

In a mixture of cadmium and zinc vapors, a fluorescence band has 
been observed which belongs neither to the Cc^ nor to the Zn 2 band 
systems. It is excited by light of wavelengths between 2150 and 2300A 
and can be ascribed only to a CdZn-molecule (1544) ■ 

The fluorescence spectrum of a mixture of mercury and thallium 
vapors excited by the Hg-line 2537A contains, between 6580 and 
4296A, four groups of bands showing fine structure. Since Winans and 
Davis obtained these bands with a mercury vapor pressure of the order 
of 100 mm and a very considerable thallium pressure, each of the 
following four processes may be responsible for their emission: a 
direct excitation of HgTl-molecules which are present in the vapor; 
fluorescence of such molecules sensitized by light absorption in Hg- 
atoms or Hg 2 -molecules ; formation of excited HgTl-molecules by 
light absorption in pairs of normal Hg and Tl-atoms during a col- 
lision; formation of excited HgTl-molecules by three-body collisions 
between normal Tl-atoms and excited Hg-atoms. The fact that the 
same bands are produced by an electric discharge through a mixture 



238 DIATOMIC GASES AND VAPORS 

of mercury and thallium vapors seems to be rather in favor of the 
first assumption (1851). 

In mixtures of mercury and indium vapors and of mercury and 
zinc vapors, bands apparently originating from Hgln and HgZn- 
molecules occur in the absorption spectra. No corresponding fluo- 
rescence bands were observed, however, in addition to the fluorescence 
lines of atomic indium and zinc. Since this atomic fluorescence is 
excited by all spark lines of wavelengths below 2000A, the excitation 
must be ascribed to light absorption by mixed molecules which 
subsequently dissociate into an excited and an unexcited atom. The 
zinc fluorescence lines (the triplet 4820, 4722, and 4688A) and the 
characteristic HgZn absorption bands below 1900A are observed only 
in distilling mixed HgZn-vapor. Winans states that one would not 
expect purification by distillation to introduce a new absorption band. 
However, the assumption that diatomic HgZn-molecules should be 
formed in distilling rather than in stagnant vapor can also hardly be 
accepted as valid. The most simple hypothesis would be that the zinc 
vapor pressure was increased by heating one part of the tube in which 
the distillation was produced (1847,1853). 



K. Re-emission of Exciting Lines and Rayleigh Scattering 

81. Re-emission of Exciting Lines by Molecules'. If the density 
of saturated sodium vapor is increased beyond the point at which the 
atomic resonance radiation contracts as "surface resonance" towards 
the wall of the observation chamber, and if the D-lines used for the 
excitation are broad or even slightly self-reversed, a well-defined 
"beam fluorescence" reappears along the path of the primary ra- 
diation in the interior of the vapor.* The intensity is weak at 250° C, 
but increases rapidly when the temperature is raised to 300° C. The 
phenomenon not only has the same outward appearance as the resoi 
nance radiation excited in sodium vapor of low pressure, but, when 
resolved by a spectrograph, the radiation seems to consist of the two 
normal D-lines. However, either the width of the lines must be a good 
deal greater than that of the resonance lines, or they must be slightly 
displaced in the spectrum — otherwise they would be completely 
reabsorbed by the intervening vapor and the beam fluorescence would 

* The phenomenon can also be produced, though with low efficiency, by 
the yellow part of a continuous spectrum. 



RE-EMISSION OF EXCITING LINES BY MOLECULES 239 

be transformed into volume fluorescence. If the primary light is plane 
polarized, the Dj-line is, as usual, unpolarized in this new fluorescence, 
while the D 2 -line shows a degree of polarization of more than 30 % at 
250° C and of 20%, still, at 300° C. The normal atomic resonance 
radiation is already completely depolarized at 200° C in saturated 
sodium vapor. Furthermore, the polarization of the fluorescence is not 
noticeably affected by a magnetic field of 80 gauss with its lines of 
force parallel to the direction of observation. The polarization of the 
resonance radiation in sodium vapor of lowpressure would be complete- 
ly destroyed under these conditions (674). 

Similar observations have been made when mercury vapor at a 
pressure of 10 mm (saturated at 80° C) was irradiated with the light 
of a mercury lamp emitting a broadened resonance line 2537A: a 
new "beam fluorescence" reappeared under these conditions; its 
wavelength practically coincided with the wavelength of the resonance 
line, its polarization amounted to 22%, notwithstanding the high 
vapor pressure and the well-known depolarizing effect produced by 
atoms of the same kind, and the polarization was not altered by a 
longitudinal magnetic field of 20 gauss in the direction of observation 
(compare Section 25) (1296). 

In both cases the fluorescence originates from very loosely bound 
diatomic molecules of the van der Waals type with energy levels 
which are only slightly different from those of the free atoms. The 
molecules must be sufficiently stable to survive the average lifetime of 
the excited states, since the absorption, as well as the re-emission, of 
the lines must occur in one and the same molecule in order to produce 
the observed polarization phenomena (840,1077). 

The conditions are different if the lines which are re-emitted are 
not very nearly coincident with the atomic resonance lines but are 
absorbed by pairs of atoms in one of the processes described in 
Sections 76-80, by which excited diatomic molecules are formed. It 
has already been mentioned that the phenomenon was discovered by 
Kapuscinski in the Cda fluorescence band h between 2600 and 2900A. 
Subsequently, it has been investigated in more detail by several 
authors in the same band, in the Hg 2 -bands i (1850-2000A) and / 
(2540A), and in a band excited in thallium vapor adjoining the thal- 
lium resonance line 2768A towards greater wavelengths.* (381,710, 
7i3,7i5)- 

In the resonance spectra of genuine diatomic molecules, the 

* It is obvious that reflection of the exciting light on the walls of the vessel 
or elsewhere was carefully avoided in these experiments. 



240 



DIATOMIC GASES AND VAPORS 



exciting line (Wood's i?-line) is not distinguished by an outstanding 
intensity from the other lines of the progression; the transition pro- 
babilities from the excited state to the vibrational levels of the ground 
state depend on the eigenfunctions by which these are characterized 
and which vary considerably in the distribution of their maxima with 
the values of v" (Figure 58). If, however, the ground state N is re- 
presented by a repulsion curve, its eigenfunction has a strong maximum 
only at the turning point* ; therefore, transitions from this point into 

an excited molecular state, or 
from the excited state to this 
point, have the greatest pro- 
bability. Before a collision oc- 
curs, two atoms have a certain 
relative kinetic energy which 
enables them to approach each 
mother to a certain distance (to 
the turning point a in Figure 
83). At this point the pair can 
absorb a line of the frequency 
corresponding to the transition 
A according to the F.C. prin- 
ciple. The same line is re- 
emitted with greatest intensity 
by the vibrating stable molecule 
in state F. The emission of 
the second line corresponding to the transition A ' in Figure 83 has 
never been observed under these conditions (393). 

If the excited state also corresponds to a repulsion curve (curve R 
in Figure 83), the absorption and re-emission of a line due to the 
transition B of Figure 83 is no longer a molecular fluorescence, but a 
perturbed atomic fluorescence, as explained in Section 36. 

82. Rayleigh Scattering. It may seem to be questionable whether 
the observations described in the last section could not be interpreted 
by a mechanism of a different kind : instead of being part of a mole- 
cular fluorescence, the re-emission of the incident lines might be due to 
classical scattering by atoms; it would not be due to the strong 
emission by relatively few excited molecules, but to the forced vi- 
brations induced in normal atoms. The amplitudes of these vibrations 

* In the language of the classical theory, this corresponds to the fact that 
the colliding molecules remain longesf at the point of their closest approach, 
where their relative velocity becomes zero. 




Fig. 83. Potential curves and eigen- 
functions of molecules formed in a 
collision process [Finkelnburg (393)]. 



RAYLEIGH SCATTERING 241 

remain small if the frequency of the scattered light differs appreciably 
from the resonance frequency of the atoms; on the other hand, the 
number of the atoms is exceedingly large in comparison to that of the 
excited molecules. 

Rayleigh scattering must occur under all circumstances. The only 
question is whether its intensity is sufficient to explain the phenomena 
completely, or whether it is at least capable of providing a considerable 
contribution. The answer to both questions is negative for the re- 
emission of the D-lines and the mercury resonance line by sodium or 
mercury vapor of great density. The luminous intensity of the D-line 
re-emission is quenched by the addition of nitrogen to the sodium 
vapor as strongly as the normal sodium resonance radiation, whereas 
the intensity of scattered radiation would not be influenced by the 
addition of a small amount of a foreign gas by which the shape of the 
absorption line is not appreciably affected. Furthermore, the duration 
of the emission process has been measured by means of a fluorometer 
and has been found to be of the same order of magnitude as that of the 
resonance radiation, while a scattering process would be "instan- 
taneous" or, at least, much shorter than 10~ 8 sec. Similar experiments 
concerning the re-emission of the mercury line 2537A lead to the 
conclusion that in either case the contribution of Rayleigh scattering 
is relatively very small and molecular fluorescence alone is to be 
taken into account. 

Landsberg and Mandelstam have carried out very detailed 
quantitative investigations on the behavior of mercury vapor at a 
pressure of 123 mm (270° C) excited by the zinc line 2558A. They 
confirm the re-emission of the line superimposed on the fluorescence 
band /. The band and the line are considerably weakened by the 
addition of hydrogen, but, whereas the band is completely quenched 
at greater hydrogen pressures, the intensity of the line tends towards 
a limiting value amounting to about 25 % of its maximum intensity. 
Furthermore, this persistent radiation is polarized to almost 100%, 
while the degree of polarization of the radiation is relatively small in 
the absence of hydrogen. 

The intensity of the line, which is still observed at a hydrogen 
pressure of 400 mm, is in perfect agreement with the equation which 
is obtained by the classical theory for the light scattered by a gas of 
refractive index n and with a number Z of scattering atoms per cc : 

7.(n— 1) 2 /2A 4 * (55) 

* The so-called depolarizing coefficient Q which occurs in the complete 
equation for light scattering isequal to 1 within the accuracy of the measurements. 



242 DIATOMIC GASES AND VAPORS 

As postulated by the equation, the observed intensity is proportional 
to the first power of the vapor density, while the intensity of the mole- 
cular fluorescence increases with the square of the density. 

These joint data leave no doubt that the persistent part of the 
re-emission of the line 2558A by mercury vapor is actually due to 
Rayleigh scattering (859,860). 

Also in agreement with the theory, the scattered intensity of the 
zinc line 2502A, on the short-wavelength side of the mercury reso- 
nance line, is about 12 times weaker when it is observed under 
identical experimental conditions. The value of the factor (n — l) 2 for 
mercury vapor at a pressure of 123 mm is 6.8- 10 -6 at wavelength 
2558A, and only 0.55- 10 -6 at 2502A; in the same wavelength range, 
the factor 1/A 4 varies by not more than 8 %. 

In this connection, a phenomenon which Wood observed at a 
much earlier date must be mentioned. The iron line 2535. 6A is reflected 
geometrically and without change of frequency at the boundary 
between mercury vapor of high pressure and the quartz window of the 
tube containing the vapor. The geometrical reflection was also ob- 
tained with the short-wavelength half of a strongly self-reversed 
mercury resonance line 2537A. Rump later succeeded in showing that 
this phenomenon can be followed with decreasing intensity down to 
much smaller vapor pressures at which a diffuse surface-resonance 
emission already becomes noticeable, and Schmettler proved that the 
regular reflection is not quenched by the addition of hydrogen which 
suppresses the resonance fluorescence. The only difference between the 
reflection and the scattering consists in the fact that regular inter- 
ference of the "scattered" secondary wavelets is caused by the greater 
density of the oscillators performing forced vibrations. The geometrical 
reflection is restricted to light of wavelengths slightly shorter than that 
of the resonance line because the difference between the refractivities 
of quartz and of the mercury vapor becomes large only in this spectral 
region on account of the existence of anomalous dispersion near the 
absorption line. It is of historic interest to note that Wood was led 
to the discovery of resonance radiation by looking for geometrical 
reflection by a vapor, which could be expected according to the laws 
of classical optics (190,1394,1440,1866,1874,1887,1906). 

Landsberg and Mandelstam point out that the re-emission of 
lines mentioned in the preceding section can be partially due to 
Rayleigh scattering even in cases where the frequencies of the lines 
differ from the resonance frequencies of the absorbing vapors by 
much larger amounts. Equation (55) does not contain the difference 



RAYLEIGH SCATTERING 243 

between the two frequencies, but the factor (n — l) 2 , which is related 
only indirectly to the difference between the frequencies of the 
scattered line and the absorption line. For mercury vapor of 100 mm, 
this factor varies between 5. 1 and 4 • 10 -6 in the spectral region between 
2100 and 2164A, in which Faterson observed the re-emission of a 
number of lines (the Zn-lines 2100, 2139, and 2164A and the Cd-line 
2144A) and thus is of the same order of magnitude as for the line 
2558A. The re-emission of the aluminum lines below 1990A becomes 
noticeable at much lower vapor pressures; the refractive index of 
the vapor has not been determined in this instance, but it must 
be expected to be very large considering the close neighborhood of 
the mercury resonance line 1849A, which is about ten times stronger 
than the line 2537A {350,433). 

It is not improbable that a part of the line re-emission in cadmium 
and thallium vapors is due to the scattering process which has been 
proved to be effective at least for some lines re-emitted by mercury 
vapor. In the main, however, the phenomenon is caused by molecular 
fluorescence even in the case of mercury vapor, as long as the fluo- 
rescence is not quenched by the presence of hydrogen. In Cd-vapor, 
the contribution of scattering to the total re-emission must be still 
smaller if the observation concerning the equal polarization of the lines 
and the underlying bands is correct. 



CHAPTER III 

POLYATOMIC GASES AND VAPORS 

A. Types of Fluorescence Spectra and the Energy Relations 

83. Some Distinguishing Properties of Polyatomic Molecules. For 

many reasons the fluorescence spectra of polyatomic compounds are 
much more complicated than the resonance spectra of diatomic 
molecules, and, accordingly, their interpretation is much more 
difficult. 

a. Instead of only one vibrational frequency, several frequencies 
and their possible combinations are superimposed on every elec- 
tronic frequency. Therefore, the sum of all possible transitions, even 
from a single level of an excited state to the ground state, no longer 
corresponds to a progression of singlets or doublets, but to a sequence 
of more or less complex band groups showing little regularity. 

b. Instead of a single principal axis of inertia, the molecule has 
three such axes and, therefore, three rotational frequencies, each 
with its separate rotational quantum numbers. The rotational doublet 
itself is thus replaced by a group of lines ; for asymmetrical molecules, 
a further complication is caused by the fact that the selection rule for 
J is not strictly valid. 

c. The electronic energy levels are, in general, more numerous and 
separated by smaller intervals. In compounds consisting of several 
radicals, the electronic states of the individual components are often 
preserved almost unaltered and independent of each other. 

d. The possibility of a direct photodissociation is the greater, the 
larger the number of components forming the molecule; simul- 
taneously, the number of possible predissociation processes increases. 
Therefore, continuous and diffuse bands without fine structure, in 
which light absorption produces no fluorescence,* are numerous in 
the absorption spectra of polyatomic molecules. The number of such 
molecules which have only continuous or diffuse absorption bands is 
very much larger than in the case of diatomic molecules. On the other 

* Fluorescence which may occur in one of the dissociation products 
originating from a photodissociation is, of course, not considered here. 

244 



DISTINGUISHING PROPERTIES OF POLYATOMIC MOLECULES 245 

hand, the emission of continuous fluorescence bands is caused, again 
by transitions from an excited state into a state represented by a 
repulsion curve. It is, however, often impossible to decide whether 
an absorption or emission band of a polyatomic molecule is genuinely 
Continuous, or whether it only appears as continuous because its 
overlapping individual lines cannot be resolved. 

e. Bands showing fine structure occur in the absorption spectra 
of polyatomic molecules which are not excited to fluorescence by light 
absorption in these bands. If the absorption bands are relatively weak 
and the probability <xj of the corresponding transition small (e.g., lja t 
= t 2 = 10 -6 sec), the light emission is practically suppressed by a 
competing radiationless process which has a probability a 2 with t 2 = 
10~ 8 sec. This lifetime of the excited state corresponds to the same 
natural line width as that of a normal "allowed" atomic line. Even 
by shortening the lifetime to 10~ 10 sec, the lines are not broadened 
appreciably beyond their width caused by Doppler effect at room 
temperature. If a x and a 2 are of the same order of magnitude, fluo- 
rescence is observed with considerable intensity, although its yield 
is more or less reduced by the competing process. 

f. In diatomic molecules the only type of "competing radiation- 
less processes" mentioned in paragraph (e) is predissociation. In 
polyatomic molecules "internal conversion" is even of greater im 
portance. The existence of a second competing process is proved by 
the fact that neither fluorescence nor photolysis is produced by ir- 
radiating certain compounds, such as crotonaldehyde, which has 
discontinuous and continuous absorption bands in the near u.v. ; in 
many other cases, the total yield of fluorescence plus photodissociation 
remains far below 100%, so that the surplus energy must be lost by 
another process. As already stated under d, the vibrational and ro- 
tational levels of the electronic ground state and the excited state are 
frequently so tightly packed that a perfect energy resonance always 
exists between some high vibrational level of the ground state and a 
given level of the excited state. Because of the F.C. principle, this is, 
in general, by no means sufficient to allow a transition from one to the 
other. However, if a nuclear configuration which is common to both 
states can be attained, so that the transition can occur without 
changing the position and the momentum of the nuclei, then the 
transition can have a great probability. This means, in the representa- 
tion by polydimensional 'potential surfaces which, for polyatomic 
molecules, replace the simple potential curves, that the surfaces 
belonging to the ground state and the excited state, respectively, 
Pringsheim 9 



246 



POLYATOMIC GASES AND VAPORS 



must intersect or at least touch each other; or, making use of the 
simplified representation by two-dimensional "configuration coordi- 
nates" (compare Section 38) : the transition can take place only at 
the intersection of the two curves iVand A (Figure 84). The probability 
of a passage from A into N depends chiefly on the average time 8 
within which the excited molecule reaches the crossing-point C in 
its motion along the curve A . When the molecule passes from A to N, 
the total excitation energy is transformed into vibrational energy of 
the ground state and is subsequently transferred by collisions to other 

molecules. Because of the part 
played by collisions in the final 
dissipation of the energy, internal 
conversion is of special importance 
for condensed media. If this final 
dissipation by collisions or infrared 
radiation does not take place, the 
energy must remain in the mole- 
cule, which can thus eventually 
return into the excited electronic 
state (414,1145). 

g. The light absorption by a 
molecule occurs at a moment at 
which its nuclei are in a certain for- 
tuitous configuration; the excited 
state reached from this configu- 
ration with greatest probability is 
determined by the Franck-Condon 
principle. If the amplitude of one 
of the fundamental vibrations thus attained in the excited electronic 
state is large, due to its anharmonicity this vibration will be suf- 
ficiently coupled with the other fundamental vibrations of the mole- 
cule so that the repartition of energy between the various vibrational 
degrees of freedom varies constantly: the molecule performs a 
"Lissajous movement" on the polydimensional potential surface. 
While a diatomic molecule is found most probably at a turning point 
of its excited oscillation, it may take a long time before a polyatomic 
molecule comes back to a given point of its potential surface, or 
before the same phase relation of all its fundamental oscillations is 
again attained simultaneously. If the return from many points of 
the "Lissajous figure" in the excited state to corresponding nuclear 
configurations in the ground state is possible, the structure of the 




Fig. 84. Configuration potential 
curves for internal conversion. 



stokes' law and the selection rules 247 

emission band will be so complicated that it appears to be contiuoous 
and the exciting line, or a resonance series originating from this line, 
will not stand out on the continuous background. If, on the other 
hand, only one of the fundamental vibrations is strongly coupled 
with the electronic transition (in other words, if the strength of only 
one bond responsible for one of the vibrations differs widely in the 
two states) a considerable part of the oscillation energy may remain 
in the molecule when the electron returns to the ground state. This 
is another reason, not dependent on collisions but rather caused by 
a kind of internal conversion, why the fluorescence spectra of poly- 
atomic molecules do not overlap the absorption bands; the whole 
vibrational structure of the two spectra may, for this reason, also be 
considerably different. 

h. In diatomic vapors the quenching by induced predissociation 
becomes less effective if a part of the excited molecules is transferred 
into lower vibrational levels by the collisions; thus, the long-wave- 
length part of a fluorescence band can even be enhanced. In polyatomic 
molecules analogous processes occur with much greater efficiency 
because, in general, the time elapsing before the "crossing-point" is 
reached is longer. If the fluorescence of a vapor at low pressure is very 
little excited by the absorption of light which produces almost ex- 
clusively predissociation or internal conversion, the total fluorescence 
yield can be increased many times by the addition of a foreign gas 
of atmospheric pressure. This "stabilizing effect" of collisions is again 
of special importance in liquid solutions where, very frequently, the 
fluorescence of polyatomic molecules is excited by light of much shorter 
wavelengths than the fluorescence of the same compound in the vapor 
state (1648,1745). 

84. Stokes' Law and the Selection Rules. Frequently, the discon- 
tinuous absorption bands of polyatomic molecules which correspond to 
transitions into an excited state with quantized vibrational levels are 
relatively weak. Therefore, the vapor pressures must be high in order 
to provide absorption of sufficient intensity: in many vapors, fluo- 
rescence cannot be observed at pressures below 50 to 100 mm. Under 
these conditions, an almost complete exchange of vibrational energy 
between the excited molecules and the molecules of the surrounding 
gas is unavoidable ; thus, the fluorescence does not originate from the 
vibrational level which has been directly reached by the absorption 
process, but from one of the lowest vibrational levels, or even from the 
nonvibrating state. For this reason, Stokes' law seems to be obeyed in 
a stricter sense in almost all fluorescence spectra of polyatomic 
Pringsheim 9* 



248 POLYATOMIC GASES AND VAPORS 

compounds than in those of diatomic molecules. The emission and 
absorption bands do not coincide over a large spectral region, but the 
former are shifted, as a whole, in the direction of greater wavelengths 
and overlap the absorption bands only slightly. The emission spectra 
consists essentially of the progression 0' -> 0", 1", 2" . . ., and the ab- 
sorption spectra of the progression 0', 1 ', 2' . . . ■<- 0"; only the band 
0' 5± 0" is common to both. The fluorescence spectrum is practically 
independent of the wavelength of the exciting radiation. 

Only if the intensity of the fluorescence is still sufficient for 
observation at low vapor pressures is the appearance of the emission 
spectrum essentially different: now, most of the emission bands 
originate from the higher vibrational level which has been directly 
excited and, moreover, the selection rules are, in general, not the same 
for v' = and for v' > 0. 

According to the main principle governing the selection rules, 
in a radiating transition between two states the symmetry properties 
of the eigenfunctions which characterize the various states of a 
polyatomic molecule must again remain unaltered with respect to the 
symmetry elements of the molecule (planes, axes, or centers of 
symmetry) . 

The nuclear vibrations of diatomic molecules are always parallel 
to the line joining the nuclei and do not affect the symmetry of the 
molecule. In polyatomic molecules the vibrations are either symmetri- 
cal (with quantum numbers v s ) or antisymmetrical (with quantum 
numbers v a ). If, for instance, a molecule is planar, the plane of the 
molecule is a plane of symmetry, since the mirror image of the mole- 
cule reflected on this plane is the molecule itself. In the model of the 
formaldehyde molecule drawn in Figure 85, not only the plane XZ 
of the molecule, but also the plane XY are planes of symmetry. An 
oscillation which is confined to the plane XZ is symmetrical with 
respect to this plane; the oscillation indicated in the figure by full 
arrows is also symmetrical with respect to XY and, thus, is "totally 
symmetrical " (symmetrical with respect to all existing elements of 
symmetry). Any oscillation with a component parallel to the Y-axis 
is antisymmetrical with respect to the plane XZ ; on the other hand, 
the oscillation lying in the plane XZ which is indicated by dotted 
arrows in Figure 85 is antisymmetrical with respect to the 
plane XY. 

If a molecule is initially in a nonvibrating state, only the value of 
v s can be altered in an allowed electronic transition which by itself 
leaves the symmetry of the molecule unaffected, while all Av a are 



stokes' law and the selection rules 



249 




Fig. 85. Symmetrical and 
antisymmetrical vibra- 
tions of the formaldehyde 
molecule. 



equal to 0. This follows clearly from the F.C. principle in its original 

form. If in the electronic transition the symmetry of the molecule as a 

whole is preserved, the positions of equilibrium of the individual 

atoms in the two electronics states can differ only insofar as the total 

symmetry of the molecule is not affected by such changes. If the 

equilibrium positions of the various nuclei were displaced in Figure 85 

along the dotted arrows, which represent 

an antisymmetric vibration, the symmetry 

of the molecule with respect to the plane 

XY would be lost. On the other hand, a 

displacement of the equilibrium positions 

of the nuclei along the solid arrows would 

not alter the symmetry of the molecule. 

If, however, vibrational levels are already 

excited in the initial state of the molecules, 

v a can alter by an even number of quanta 

[Av a = 0, 2, 4 . . .) simultaneously with 

an allowed electronic transition, since the 

eigenfunctions of antisymmetrical vibrations are all symmetrical for 

even values of v a and antisymmetrical for odd values of v a . 

Because of these selection rules, a monochromatically excited 
"resonance spectrum" may appear to be more complicated in certain 
respects than the fluorescence spectrum which is obtained under the 
same conditions of excitation, if all molecules are transferred into the 
nonvibrating state by collisions before the emissions takes place. The 
individual bands contain more rotational lines in the second case, 
since new rotational levels are populated by the collisions, but only 
bands which correspond to a variation of the quantum numbers of the 
relatively few totally symmetrical oscillations appear in the fluo- 
rescence spectrum. The "resonance spectrum" contains, in addition 
to these, the numerous bands corresponding to Av a = 2,4 . . . The 
spacings of the progressions caused by the variations of v a are twice 
as large as the fundamental vibrational frequencies. 

If the electronic transition is forbidden, because by itself it 
would alter the symmetry of the molecule, it becomes allowed, to 
a certain degree, if it is combined with a vibrational transition which 
by itself would also change the symmetry. In particular, "forbidden 
transitions" from a nonvibrating initial state can occur, corresponding 
to Av a = 1, 3, 5 . . ., while the O'-O" band is missing. Accordingly, 
the absorption and the fluorescence bands do not overlap but are 
separated by an interval. Considering the low intensity of many bands 



250 POLYATOMIC GASES AND VAPORS 

which show fine structure in the absorption spectra of polyatomic 
molecules, it is probable that such bands frequently correspond to 
forbidden electronic transitions. In several instances this assumption 
is supported by the theoretical treatment of the spectrum. 

In addition to the selection rules which are derived from the 
symmetry relations, the transition probabilities are again subjected 
to the Franck-Condon principle, as has been pointed out in Section 83g. 



B. Fluorescence Spectra of Polyatomic Molecules 

85. Inorganic Compounds. Fluorescence of the vapors of inorganic 
polyatomic compounds has been observed in a very few instances. 
This is only to a smaller degree due to the fact that the first absorption 
bands are usually situated in the far u.v., as in the case of C0 2 and 
NH 3 , and are accessible only to vacuum spectrography. The more 
general reason seems to be that, according to the tables compiled by 
Sponer and Teller,* most of the molecules have only continuous ab- 
sorption bands, even fluctuations being relatively scarce. 

Somewhat detailed data are available concerning the fluorescence 
of N0 2 and,S0 2 . The absorption spectrum of nitrogen dioxide consists 
of a weak and very intricate system of bands between 5750 and 3520A, 
and a second system between 2600 and 2270A. Both systems show 
fine structure. Irradiation with light of wavelength below 3800A 
produces no fluorescence, but only dissociation. However, a fairly 
strong visible fluorescence is excited by irradiation with light of 
A > 4000A. The emission spectrum consists of two bands at 6550- 
6250A and 6050-5600A,f followed by a few weaker narrow bands 
reaching into the blue region. The fluorescence intensity increases 
with the vapor pressure up to 1 mm, due to the increasing absorption 
of the exciting light, and drops very slowly at higher pressures ; surface 
fluorescence remains visible even at pressures of 90-100 mm. The 
quantum yield, however, has its optimum Q at the very lowest vapor 
density and has already dropped to \Q at a pressure of 0.02 mm of 
N0 2 (Figure 86). A similar strong quenching is produced by the 
addition of C0 2 , while N 2 , 2 , and H 2 are a little less effective, with 
half-value pressures p* between 0.04 and 0.06 mm. The apparent 
quenching efficiency of the foreign gases is again dependent on the 

* H. Sponer and E. Teller, Rev. Modern Phys., 13, 75-170 (1941) (1545a)- 
t A fine structure observed in the second of these bands seems to be 
caused, at least partially, by the overlapping absorption bands. 



FLUORESCENCE SPECTRA OF INORGANIC COMPOUNDS 



251 



N0 2 -pressure itself, as in the case of the visible I 2 -fluorescence. The 
great sensitivity to collisions is caused not by anomalously large 
quenching cross sections (they correspond very nearly to the kinetic 
cross sections) but by a lifetime of the excited state of the order of 
10~ 5 sec. This is in agreement with the low absorption coefficient 
characterizing the N0 2 -bands, which is about 100 times smaller than 
that of the visible I 2 -bands. Moreover, the long lifetime has been 
proved experimentally: at a low vapor pressure at which the mean 



too 

80 
60 

20 

O 
0.1 



i i i r — ■ — i 1 — 1 



10 100 1000 

p in mm 



Fig. 86. Intensity and yield of the fluorescence of 

N0 2 as a function of the gas pressure (Baxter). 

I : intensity. Q, : relative yield 



free paths are equal to 1 cm, the boundaries of the fluorescent beam 
became diffuse, while they were sharply defined at a pressure of 4 mm 

(74,593,1144) ■ 

The intensity distribution in the fluorescence spectrum depends 

on the wavelength of the exciting light : under excitation by the mer- 
cury line 4358A the red fluorescence band prevails, while under ex- 
citation by the mercury line 4047A higher vibrational levels of the 
upper electronic state are populated and the yellow-green band is 
emitted almost exclusively. Apparently the strong quenching action 
of collisions prevents a redistribution over the various vibrational 
levels. Notwithstanding this fact, the fluorescence is completely 
depolarized, as might be expected because of its slow decay. Irradia- 
tion with the violet mercury line produces predissociation in compe- 
tition with the fluorescence ; the blue line excites only fluorescence. 

S0 2 -vapor exhibits, also, several u.v. absorption band systems. 
The first system between 3900 and 2600A is rather weak, and, although 



252 POLYATOMIC GASES AND VAPORS 

the bands show a well-defined fine structure, they do not seem to be 
connected with the excitation of fluorescence. The second system 
stretches from 2440 to 2000A; the vapor is dissociated by the ab- 
sorption of light of wavelengths below 21 00A, but spark lines of greater 
wavelength (e.g., Cu 2136, 2190, and 2225A, Ni 2169 and 2207A, 
Cr 2171A, Cd 2195A, Pb 2204A, and Zn 2100A) excite long sequences 
of fluorescence line groups extending from the exciting line to the 
violet. Especially in their long- wavelength parts, they are very 
difficult to analyze. The complexity of the spectra may, in part, be 
due to the fact that every exciting line covers several absorption lines, 
but may be attributed even more probably to the various reasons 
mentioned in the preceding section. The fluorescence spectrum excited 
by the Zn-line 2 100 A has a relatively simple structure in which the 
three frequency differences of 1370, 1 150, and 520 cm -1 recur periodi- 
cally; they correspond to three fundamental frequencies of the un- 
excited molecule which have been observed in the S0 2 Raman 
spectrum. The same periods are found, although not so obviously, in 
some of the other resonance series and, furthermore, they agree with 
the analysis of the absorption spectrum (961,1521). 

By the addition of foreign gases (A, H 2 , or 2 ), the resonance 
progressions are not transformed into the complete band spectrum. 
The intensity of the fluorescence is very little reduced by argon of 
100 mm and the quenching efficiency of hydrogen and oxygen is also 
relatively small. It is compensated for, in part, by increasing absorption 
of the primary light due to the broadening of the absorption lines. If 
this enhancing effect is taken into account, 400 mm of C0 2 quench the 
fluorescence to about 1 / 50 of its initial value, if it is excited by the 
group of copper lines 2136-2225A, while the intensity is decreased 
only to Vio b y the addition of the same quantity of C0 2 , if the fluo- 
rescence is excited by the Zn-line 2100A. In the latter case the lifetime 
of the excited state is already shortened, apparently by predissociation, 
since the zinc line lies very near to the predissociation limit, beyond 
which no fluorescence can be excited. The Pb-line 2088A and the Ag- 
line 2066A are quite ineffective in producing fluorescence in S0 2 - 
vapor. 

No fluorescence has been observed in the gases C0 2 and CS 2 . The 
question has been discussed, whether the infrared radiation of carbon 
dioxide at high temperatures should not be regarded as resonance 
radiation which is excited by the radiation coming from the walls of 
the oven. Quantitative measurements performed by Gerlach proved 
this assumption to be wrong {488). But even lacking this experimental 



FLUORESCENCE OF ORGANIC COMPOUNDS 253 

proof it could not be doubted that, at the high pressures under which 
alone the emission can be obtained with appreciable intensity, and 
considering the small probability of emission and absorption processes 
in the infrared, the temperature equilibrium is achieved practically 
only by heat conduction and convection, and not by radiation. 

Absorption bands of ammonia and water vapor in the u.v. above 
2500A are not tabulated by Sponer and Teller. During the investi- 
gation of the Raman effect of these vapors it was found, however, 
that they are excited to fluorescence by irradiation with the mercury 
line 2537A. The emission band of ammonia reaches from 2700A far 
into the visible, while the intensity of the water- vapor band has its 
maximum close to the exiting line and drops rapidly in the direction 
toward greater wavelengths. Beyond the fact that the bands are con- 
tinuous, nothing is known concerning these last two instances of a 
fluorescence of polyatomic inorganic vapors (1342). 

86. Introductory Remarks Concerning the Fluorescence of Organic 
Compounds. Organic compounds which are known to be fluorescent 
in the vapor state are numerous. However, these are, without ex- 
ception, also fluorescent in liquid solutions or even as pure solids. Most 
investigations, in particular the earlier ones, deal primarily with the 
fluorescence of solutions, because of the smaller experimental dif- 
ficulties ; furthermore, many substances are decomposed at the temper- 
ature necessary for evaporation and others exhibit photoluminescence 
only when they are ionized. For this reason, all questions referring 
to the connection between constitution and fluorescence are tre- 
ated in later chapters and only phenomena which are specifically 
characteristic of the vapor phase are mentioned in the following 
sections. 

The preceding remarks refer mainly to aromatic compounds, 
while observations concerning the fluorescence of aliphatic or non- 
aromatic ring compounds are almost as scanty as those about inorganic 
polyatomic vapors. The reasons are essentially the same: the first 
absorption bands of many aliphatic compounds (methane, ethane, 
methanol, ethanol and other alcohols, hexane, etc.) lie in the far u.v., 
many others have only continuous absorption bands, or, if the ab- 
sorption bands show structure, the absorption process leads never- 
theless to predissociation or, perhaps, to internal conversion. The latter 
seems, for instance, to be exclusively the case for phosgene or thio- 
phosgene with a fine-structure band between 5712 and 3950A within 
which neither fluorescence nor dissociation is produced. Even in the 
vapors of aliphatic compounds in which fluorescence can be obtained 



254 POLYATOMIC GASES AND VAPORS 

the yield is, in general, relatively small and dissociation or internal 
conversion is competing with the emission process. 

87. Nonaromatic Organic Compounds. All known instances of 
fluorescent aliphatic vapors are collected in Table 45. Probably it is 
only owing to too small intensities that in several cases the "excitation 
spectra" do not seem to reach as far into the red as the absorption 
bands. On the other hand, the short-wavelength limit of the excitation 
spectra is certainly due to the predominance of competing processes in 
the wavelength region beyond this limit. 

In the absorption spectrum of formaldehyde a series of equi- 
distant bands stretches from 3530A towards shorter wavelengths with 
a spacing of 1190 cm -1 ; they have been designated by Herzberg and 
Gradstein as "A" (3530A), "B" (3400A), "C" (3270A), etc. On the 
long-wave side of "A" follows, at the appreciably larger distance of 
1225 cm -1 , a last, much weaker absorption band "a" at 3706A. 
Fluorescence is excited by absorption of light in the bands "A," "B," 
"C," with rapidly decreasing yield in passing from "A" to "C." 
The fluorescence spectrum begins with a relatively strong band which 
coincides with the absorption band "«" and extends from there far 
into the green in a long series of bands, some of which show fine 
structure (526,606). 

The total strength of the absorption and fluorescence bands is 
rather low; the fluorescence has a noticeable intensity only at vapor 
pressures above 50 mm. It is probable, therefore, that the corre- 
sponding electronic transition is forbidden and occurs only when 
combined with a simultaneous jump Av a = 1, 3, 5 ... of an anti- 
symmetrical oscillation. Since at the temperature of observation most 
of the molecules are in the nonvibrating ground state, the absorption 
bands "A," "B," "C" ... are caused by the ^-transitions 1', 3', 5' <- 
0". Only the weak band "«" originates from the electronic ground 
state with v" a = 1 and corresponds to the transition 0'*- 1". On the 
other hand, at the prevailing high pressure, all excited molecules are 
transferred by collisions into the nonvibrating level of the upper 
electronic state and the emission bands are caused by the ^-transitions 
0' -> l" (coinciding with the absorption band "a"), 0' -> 3", 5" . . . If 
this interpretation is correct, the frequency difference of 1 190 cm -1 is 
at first approximation equal to 2o>', and, thus, u>' = 595 cm -1 . The 
corresponding value of the vibrational frequency of the ground state is 
obtained (see Figure 87) from the equation : 

A — a = w" + m", or <o" = 1225 — 595 = 630 cm -1 (56) 



FLUORESCENCE OF NONAROMATIC ORGANIC COMPOUNDS 255 



-|ll90£m -1 
• u>' ■ 595 cm " 



i ui ■ 630 cm 



Fig. 87. Energy-level dia- 
gram for the fluorescence 
and absorption of formalde- 
hyde (Gradstein). 



A further period of 1700 cm -1 , which is known as the characteristic 
frequency of the C-O bond, can be found with some degree of certainty 
in the fluorescence bands, but a complete analysis of the spectrum has 
not yet been achieved. 

The fluorescence of the vapors of acetone and biacetyl has been 
the subject of much discussion. A com- 
paratively strong greenish fluorescence, 
which is observed when acetone vapor is 
irradiated with the mercury line 3 132 A, 
was ascribed at first to the acetone mole- 
cules ; at present it is supposed to belong 
to biacetyl, which is formed under the 
action of the irradiation. If the newly 
formed biacetyl is continuousy removed 
in streaming acetone vapor, only a weak 
blue fluorescence is excited under the 
same conditions. This blue luminescence 
also prevails alone in the emission spec- 
trum, if the green fluorescence is quenched 
by the addition of oxygen (11-13,25601, 
395,602 ,g62a,g8y ,1146 ,1188) . 

Since the blue acetone vapor fluorescence in the spectral region 
between 4860 and 4180A can be resolved into 26 bands with an 
average spacing of 120 cm -1 , this emission process does not seem to 
be directly related to the photodissociation of the acetone molecules 
(962a) . 

In pure biacetyl vapor the green fluorescence is excited by the 
absorption of blue and violet light which is quite ineffective in acetone 
vapor. The three emission bands listed in Table 45 show a somewhat 
irregularly spaced structure with A v ~ 55 cm -1 in the orange and 
A v ~ 85 cm -1 in the green which apparently is unrelated to the 
structure of the absorption bands. The absorption and the emission 
bands are separated by a gap (Figure 88). While the intensity of the 
absorption bands corresponds to a transition probability a x = 10 5 
sec -1 , the duration of the emission is. of the order of 10~~ 3 sec, with an 
exponential decay ; this has been proved by phosphoroscopic measure- 
ments as well as by the method of observing the diffuseness of the 
fluorescence beam at low vapor pressures. Almy assumes, therefore, 
that the molecules pass from the directly excited state F (Figure 89) 
into a metastable state M from which they are enabled by the 
thermal fluctuations to return into the lowest vibrational levels of F, 



256 



POLYATOMIC GASES AND VAPORS 



with subsequent emission of fluorescence. If excited by blue or violet 
light, the fluorescence yield is practically constant, of the order of 15 %, 
in a pressure range between 1 and 50 mm. On the other hand, the yield 
is very small at low pressures if the wavelength of the primary light is 
3650A, and increases gradually to about 13 % if the pressure is raised 
to 50 mm. This behavior suggests the additional hypothesis that 
predissociation occurs with very great probability from the high 
vibrational levels reached by the absorption of the u.v. line, and that 



6095 5572 5137 A 

A 1 I 




Fig. 88. Absorption and fluorescence spec- 
trum of biacetyl vapor at room temperature 
(Lewis and Kasha). 
a : absorption band e : molar absorption 

b: fluorescence band. coefficient 

I : in arbitrary units 



the molecules are "stabilized" to a certain degree by collisions at 
greater vapor pressures. 

Lewis modified the energy diagram presented in Figure 89 in 
that he assumed that the luminescence of biacetyl vapor is not a 
"phosphorescence" due to the re transfer from state M to a low level 
of F with a subsequent "allowed" radiating transition to N, but a 
direct "forbidden" transition from state M to state N, the former 
being a triplet and the latter a singlet state. The hypothesis is based 
on an observation of Lewis and Kasha that biacetyl dissolved in a 
solidified organic solvent emits a fluorescence with a spectrum identi- 
cal with that of the vapor* and with a mean life of 5- 10~ 3 seconds. 
Phenomena of this type are treated in Chapter V, E. The relatively 
small influence of the temperature on the lifetime is strongly in favor 
of Lewis' assumption that the luminescence is a "slow fluorescence" 
and not a phosphorescence (9276) . 

* The fluorescence spectrum of biacetyl in aqueous solution also practically 
coincides with that of the vapor. 



FLUORESCENCE OF NONAROMATIC ORGANIC COMPOUNDS 



257 




N 



[It must be pointed out here, however, that if the low transition 
probability M ->■ N is due to the fact that N and F are singlet states and 
M is a triplet state, then the transition F -> M must occur nevertheless, 
with a probability which is at least equal to 17.6 % of the sum of the 
probabilities of all others processes by which the molecules in the state 
F are quenched. If, in agreement with Almy's diagram (Figure 89), 
the competing predissociation occurs in state M, all excited molecules 
are transferred from F to M in a time shorter than 10 -7 sec, since no 
normal fluorescence due to a direct return from F to N with a yield of 
more than 1 % is observed. If, 
on the other hand, Lewis' as- 
sumption is correct and the ex- 
cited molecules which do not 
contribute to the luminescence 
are quenched while staying in 
state F, the lifetime of the latter 
cannot exceed 10~~ 7 sec, and even 
in this case the probability of the 
transition F -> M would be fairly 
high. However, if the transition 
probabilities are governed by 
the electronic selection rules, 
they are the same for the transi- 
tion F -> M in the vapor and in the solid solution ; and if, furthermore, 
the mean duration of the afterglow of 1.5- 10 -3 and 5- 10~ 3 sec can 
be accepted as correct for the vapor and the solid solution, respec- 
tively, at least 70 % of the molecules which are transferred from F 
to M are quenched in the vapor, and, therefore, not 15 but at least 
50 % of all excited molecules must pass from F to M. The corres- 
ponding transition probability is almost as large as the one derived 
from Almy's original assumption. 

Finally, the transition is spontaneous, since the quantum yield of 
the vapor fluorescence (when excited by blue and violet light) does not 
depend on the vapor pressure. Thus, the selection rule forbidding the 
radiating transition from M to N does not appreciably influence the 
spontaneous radiationless transition from F to M. ] 

After a long-lasting irradiation the fluorescence of the vapor vanis- 
hes, because the biacetyl molecules are destroyed by photochemical 
processes which may be initiated by predissociation. It is probable, ho- 
wever, that this is not the only process competing with the re-emission 
of light , but that internal conversion plays an even more important part . 



Fig. 89. Energy-level diagram for the 
luminescence of biacetyl (Almy). 



258 



POLYATOMIC GASES AND VAPORS 



While self -quenching seems to be negligible, the green biacetyl 
fluorescence is extremely sensitive to quenching by oxygen. The oxygen 
half-pressure is 1.3- 10~ 2 mm; if the irradiation is continued after the 
admission of a small quantity of oxygen, the oxygen is eventually 
used up by oxidizing processes and the fluorescence recovers its initial 
intensity. The quenching efficiency of iodine is even greater; the 
original fluorescence intensity of biacetyl vapor is reduced to less 
than 3 % by addition of iodine vapor of 2 • 10 -3 mm. 



Table 45 
Fluorescence of Aliphatic Vapors 
(Wavelengths in A) 



Compound 


Formula 


Fluorescence bands 


Discontinuous 
absorption bands* 


Excitation 
spectrum 


Formaldehyde 


COH 2 


5100-3700 
series of bands 


3700-3100 

(-2750) 


3530-3200 


Glyoxal (1655) 


(CHO) 2 


5200-4200 
continuous 


4600-3400 


4400-3600 


Methylglyoxal 




visible 


? 


? 


Acetone 


CH3COCH3 


4750 and 
biacetyl bands 


3340-2950 

(-2200) 


3300-3100 


Biacetyl 


CH 3 COCOCH 3 


broad bands 

with maxima : 

6095, 5572, 5117 


4670-3500 


4400-3650 


Acetaldehyde 


CH 3 COH 


biacetyl bands 


3485-2730 


3400-2800 


Ethyl methyl 
ketone 


C 2 H 5 COCH 3 


biacetyl bands 


3200-2400 


about 3132 


Propionaldehyde 


C 2 H 5 COH 


5460-4360f 
continuous 


? 


about 3000 


Diethyl ketone 


C 2 H 5 COC 2 H 5 


5460-4360§ 


? 


about 3000 


w-Butyraldehyde 


C 3 H 7 COH 


visible 


3400-2850 

(-2420) 


3132 


Ethylamine 


C 2 H 5 NH 2 


3600-2700 with 
max. 3435, 3285, 
3140, 3005, 2880 


2372-2300 

(-1850) 


3270-2300 



* The figures in parentheses indicate the limit of the nondiscrete bands, 
t Probably belonging to bipropionyl diketone, QjHjCOCOC^Hs. 
§ Possibly also belonging to a diketone. 



FLUORESCENCE OF NONAROMATIC ORGANIC COMPOUNDS 259 

If the biacetyl fluorescence is produced by irradiating acetone 
vapor with the mercury line 3 132 A, the intensity of the green lumi- 
nescence grows slowly to a limiting value. Pure biacetyl vapor does 
not absorb the line 3 132 A and is not excited by it; if acetone vapor is 
added to biacetyl vapor, the green fluorescence appears immediately 
with its full strength when the vapor is irradiated with the line 3 1 32 A. 
These experiments prove that the emission of the biacetyl bands by 
acetone vapor is not caused by a direct formation of excited biacetyl 
molecules, but that the biacetyl molecules are first formed by a photo- 
chemical process, and their luminescence subsequently excited as 
"sensitized fluorescence." No green fluorescence is produced in acetone 
vapor by light of A < 2900A, beyond which the discrete acetone ab- 
sorption bands merge in to a continuum. This was assumed, at first, to 
prove that the fluorescence belongs to the chemically unaltered acetone 
molecules ; in reality, the molecules are dissociated by light absorption 
in the discrete bands due to predissociation, probably according to 
the equation: 

CH 3 -CO-CH 3 + hv -> CH 3 CO + CH 3 (57) 

2-(CH 3 CO) ->CH 3 COCOCH 3 

Absorption in the continuous band of acetone gives rise to another 
dissociation process, which cannot be followed by the formation of 
biacetyl — perhaps : 

CH 3 -CO-CH 3 + hv -* CHsCO-CHj + H (58) 

The whole complex of phenomena proves very convincingly that the 
appearance of fine structure in a band can well be connected with 
predissociation, while the nonexistence of fluorescence excitation be- 
ginning at a given wavelength is an absolutely unambiguous sign for 
the prevalence of a "competing process"* (11,12,13,602). 

According to work of Rollefson and Graham, fluorescence is exited 
in the vapor of acetaldehyde at room temperature by means of irra- 
diating it with the mercury line 3132A. The fluorescence yield 

* The historical development of the biacetyl fluorescence illustrates, also, 
the danger of constructing elaborate energ5' levels for complicated molecules 
by the use of approximately agreeing numerical data. It seemed possible to 
represent the three fluorescence bands by combining the frequency of the 
exciting line with three infrared frequencies of acetone. The arbitrariness of this 
construction became evident when the fluorescence bands were proved to belong 
to another molecule. 



260 POLYATOMIC GASES AND VAPORS 

does not vary during the irradiation, but decreases with increasing 
temperature and disappears completely when the temperature 
exceeds 150° C. The decrease in fluorescence intensity is roughly 
complementary to an increase in photodissociation which competes 
with the fluorescence at all temperatures. The authors conclude from 
this behavior that the fluorescence is characteristic of acetaldehyde 
itself and not of some product of photolysis {1372). 

However, the spectrum of the fluorescence of acetaldehyde vapor, 
which Rollefson and Graham describe only as "visible," has been 
found to be identical with that of biacetyl vapor. It is true that this 
latter result was obtained by Matheson and Zabor and by Padmanab- 
han by irradiating the vapor with the nonresolved radiation from a 
quartz-mercury lamp and the photochemical production of biacetyl 
might have been due to the presence of light of shorter wavelengths. 
Thus, it is possible (although not very probable) that the fluorescence 
observed by the two groups of investigators was not of the same 
nature. Furthermore the biacetyl bands were observed in the fluo- 
rescence of the vapor of ethyl methyl ketone (C 2 H 5 COCH 3 ) (988,1188). 

Identical fluorescence spectra differing slightly from the biacetyl 
spectrum appear also upon irradiation of the vapors of diethyl ketone 
(C 2 H 6 COC 2 H 5 ) and propionaldehyde (C 2 H 5 COH). Probably the me- 
chanism is analogous in all these cases to the excitation of the biacetyl 
bands by irradiation of acetone. In the last instances mentioned above, 
the carrier of the fluorescence, according to this assumption, should be 
bipropionyl diketone. Terenin supposes that the fluorescence which 
he observed in the vapor of ethylamine should possibly also rather be 
ascribed to diethylamine. Although very little is known about the 
weak fluorescence of w-butyraldehyde, it seems plausible to assume 
that it also originates from a compound produced by a primary photo- 
chemical reaction. No fluorescence has been observed in the vapors of 
isobutyraldehyde, acrolein, or of methylamine. Thus, only a few of 
the not too numerous cases of fluorescence listed in Table 45 are 
caused by the direct excitation of an aliphatic vapor (62,454,988, 
1188,1639,1656). 

None of the nonaromatic heterocyclic single-ring compounds, 
pyrrole (C 4 H 5 N), furan (C 4 H 4 0), thiophene (C 4 H 4 S), and pyridine 
(C S H 5 N) can be excited to fluorescence in the vapor state, although at 
least the four last-named compounds have strong absorption bands 
with fine structure in the region between 3500 and 2000A (390). Only 
when they are joined to a benzene ring, as in quinoline or indole, do 
the compounds become weakly fluorescent, notwithstanding the fact 



FLUORESCENCE OF NON AROMATIC ORGANIC COMPOUNDS 261 

that the absorption bands of quinoline are much more diffuse than 
those of pyridine, which is one of the components of the quinoline 
molecule. 

88. Benzene. The fluorescence of benzene vapor is excited by 
light absorption in a relatively weak band between 2700 and 2200A. 
Light absorption in the much stronger bands in the far u.v. always 
leads to photochemical disintegration. The production of hydrogen by 
irradiating benzene vapor with light of wavelengths below 2000A 
actually was observed by Prileshajewa. 

The great complexity of the band system with its 0"-0' band 
at 39,089 cm -1 (2557.5A) is caused by the superposition of numerous 
vibrational frequencies and rotational fine structure. Various in- 
vestigators who have undertaken the analysis of the system disagree 
among themselves, more or less, in the assignment of numerical values 
to the occurring frequencies and their interpretations, and more than 
one electronic transition has even been assumed to be responsible for 
the band structure. The most recent analysis is due to H. Sponer, 
Nordheim, Sklar, and Teller; it is followed here, although it may not 
represent the final solution of the difficult problem. In this analysis, 
the band system is ascribed to a single forbidden electronic tran- 
sition {601,646,647,782,783,1500,1545). 

The fluorescence has been observed both at high pressure 
(p > 10 mm) of the benzene vapor itself or of an inactive foreign gas, 
and at low pressure {p = 0.3 mm). In the first case, the emission 
spectrum is independent of the wavelength of the exciting light, be- 
cause the excited molecules are always transferred into the lowest 
vibrational levels of the upper electronic state; identical fluorescence 
spectra have been obtained by irradiating the vapor with light from 
a quartz mercury arc, from a Cd- or Zn-spark, or from a hydrogen 
discharge tube. In the second case, the so-called resonance spectrum 
originates exclusively from the directly excited vibrational levels. 
However, the spectrum shows no likeness to the clear simplicity of 
iodine resonance progressions, because too many combinations of 
vibrational oscillations contribute to the emission process (646,647, 
ioo3,i2g4,i35o). 

Heavy benzene, or hexadeuterobenzene (C 6 D 6 ), behaves exactly 
like ordinary benzene, with the sole exception that all frequencies are 
somewhat different. Therefore, it suffices to deal in the main only with 
normal benzene (255). 

According to Sponer and her collaborators, the most important 
features of the absorption and fluorescence spectra can be represented 



262 



POLYATOMIC GASES AND VAPORS 



by taking into account only three vibrational carbon frequencies of the 
excited and of the ground state. In Table 46 and Figures 90 and 91, 
the frequencies w and quantum numbers v of totally symmetrical 
vibrations are marked by even subscripts (0, 2 . . .), those of anti- 
symmetrical oscillations by odd subscripts (1,3...). 

Table 46 

Electronic and Vibrational Frequencies (v and co) Characterizing 

the Fluorescence Spectra of C 6 H 6 and C 6 D 6 



a>o 



0>i 



co 2 



(Da 



co. 



C„H 6 38089 992 923 606 520 4 00 240 (1590) (1480) (3062) (2565) 

C 6 D 6 38292 947 878 579 497 370* 230* 

* Only the difference co" — to = 140 is actually known. 

At high pressures the excited molecules are supposed to be almost 
completely transferred into the vibrational levels v = 0, v x = or 1, 
and v 2 = 0, 1 ,2, 3, 4. The lowest of these levels have the greatest 
populations. Since the electronic transition is forbidden, only bands 
with Av l = 1,3,5... can have an appreciable intensity. Bands 
corresponding to any value of /Island Av 2 (variation of the symmetrical 



3! 



113a 



620i 



B B" 



123 1 



1520 



c.x: 



1606 ~ " 
1606 



3f 



1598 
4Q6t~ 



}240 
|923 



Al 0' A' 0' 



400 
606 



Fig. 90. Energy-level diagrams for fluorescence of benzene. 
a: high-pressure fluorescence excited by Hg-line 2537A. 
b : resonance spectrum excited by Hg-line 2537A at low 
vapor pressure. 



BENZENE SPECTRA 263 

vibration quanta) can be superimposed on the bands caused by the 
variation of v t . The level diagram of Figure 90a shows the principal 
types of bands resulting from this mechanism. The designations are, 
in the main, those of Sponer's paper: the bands designated by A, B, C, 
and D correspond to certain values of v[ and v" 2 the subscripts in A^, 
A 01 , etc., in this figure, refer to the values of v and v" , respectively. 
Since, according to our assumptions all bands in the fluorescence 
spectrum start from the level v = and lead to numerous levels v" = 
0, 1, 2, 3 . . ., the bands A^., and similarly the bands B^., C^-, and 
D^", form progressions with the spacing A v = 992 cm -1 .* They are 
the most outstanding feature of the fluorescence spectrum. (Right- 
hand part of Figure 90«). The bands B, which originate from the 
lowest vibrational level of the excited state, have the greatest inten- 
sity. The frequency differences between B and the other bands are 
(left-hand part of Figure 90a) : 

B — A = -1126; B — C= -1040; B — D = 114 cm.- 1 

These frequency differences appear as regularly recurring periods in 
the spectrum. The same is true for the difference A — D = 1212 cm -1 , 
which is twice the value of the fundamental antisymmetric frequency 
606 cmr 1 . 

Finally, a small period of 160 cm -1 is produced by the transitions 
between the excited vibrational levels v' 2 a> 2 and the levels v' 2 <^ of the 
ground state. <o 2 is symmetrical and Av^ is always zero. This causes the 
appearance of sub-bands with a spacing A v = 400 — 240 = 160 cm -1 
in every one of the bands A, B, C, and D. The superscripts in B^, 
2?oo> etc., refer to the values of v 2 = v" 2 (Figure 90«, central part). 
Thus, the fluorescence spectrum can be represented by the equation: 

v = 38039 + i/-520 — /-606 — v~-992 — v" (400 — 240) 
with v i — 0,1,2; v\ — v\ = ± 1; v = 0,1,2 . . .; w' = 0,1,2, . . . 6. (59) 

Although this analysis explains most of the more conspicuous 
bands, it is far fromdisentanglingthe whole complexity of the spectrum. 
Transitions with Av x = 3 and 5, leading to the higher levels of the 
antisymmetrical oscillation 606 cm -1 of the ground state, must also 
occur, and the other vibrations of the ground state, e.g., the a- 
symmetrical carbon vibration a>" 3 (1590 cm -1 ) which coincides almost 
exactly with the sum 992 + 606 = 1598 cm -1 , and the totally 

* The corresponding progressions in the absorption spectrum have the 
spacing 923 cm -1 . 



264 



POLYATOMIC GASES AND VAPORS 



symmetrical hydrogen vibration 3062 cm -1 , cannot be neglected 
altogether.* Besides, the bands have a rotational fine structure which 
is, in general, not quite resolved. Figure 9la gives a schematic repre- 
sentation of the small region of the fluorescence spectrum between 
2660-2 700 A and shows the great number of bands which are not 
accounted for by Equation (59). 



^14} 



37 500 



37 400 



37 30O 



37 200 



37 100 



37 000 cm 



Fig. 91. Schematic representation of part of benzene fluorescence 
spectrum (Ingold and Wilson). 
a: fluorescence spectrum at high vapor pressure. 
6: resonance spectrum at low vapor pressure. 

At high benzene pressures the first band group, between 38,600 
and 37,600 cm"" 1 (2590-2659A), containing the bands A^, C M , and B 10 , 
is missing in the fluorescence spectrum on account of reabsorption. 
If, however, the "transferring collisions" are produced in benzene 
vapor of low pressure by addition of foreign gases, these bands appear 
with fairly great intensities, though with somewhat irregular intensity 
distribution, which is caused by the still-prevailing reabsorption of 
certain sub-bands (10,1843). (For instance, the band A° m is more 
strongly absorbed than the band A]^, etc.). 

* Though not explicitly mentioned in the analysis of the fluorescence 
spectrum, the bands originating from the excited level v' = 1, also seem to be 
rather strong, as shown in Figure 6 of Sponer's paper. 



BENZENE SPECTRA 265 

The so-called resonance spectrum is by no means less complex, 
and shows rather less regularity in its structure (Figure 916). It is 
unfortunate that, for technical reasons, resonance spectra in light and 
heavy benzene have been obtained only by excitation with the mercury- 
line 2537A.* This line Jies between two rather weak absorption bands 
of light benzene vapor ; the two bands are indicated in Figure 906 as 
C\ and A^. Their small intensity, especially at low vapor pressures, 
results from the fact that they originate from the vibrational levels 606 
and 400 cm -1 , respectively. The periods 992 cm -1 (between C 10 and C u ) 
and of 1212 cm -1 (between C° 10 and X° 10 ) also appear in the resonance 
spectrum, while the period 160 cm -1 is missing because v" 2 has the same 
value in all bands. On the other hand, the bands originating from the 
excited level (923 + 520 + 240) cm -1 , which is reached by the second 
possible absorption process, fall in between the first two progressions 
(left-hand side of Figure 906). Besides, there are, again, transitions to 
additional levels of the ground state (e.g., 1598 or 3062 cm -1 ), which 
make the appearance of the spectrum still more complicated. 

In this respect heavy benzene is slightly more favorable: the 
mercury line coincides with the absorption band (2 • 479 + 230) ■<- 
(579 + 370) cm -1 , so that the emission bands originate almost ex- 
clusively from one and the same upper level; as a matter of fact, the 
resonance spectrum of heavy benzene is decidedly simpler than that 
of normal benzene. 

The fluorescence of benzene vapor is affected very little by self- 
quenching, and the quenching efficiency of foreign gases (He, N 2 , 
C0 2 , cyclohexane, and even atmospheric air) is relatively small; 
transferring collisions by which the "resonance spectrum" is trans- 
formed into the "fluorescence spectrum" have by far the greater 
probability. If, however, the temperature is raised to 200° C at constant 
vaporpressure, the fluorescence becomes much weaker and its structure 
more diffuse; at 400° C, the fluorescence spectrum consists only of a 
faint continuous band. Simultaneously, the diffuseness characteristic 
of strong predissociation extends more and more from the short-wave 
absorption bands towards bands of greater wavelengths. Even at room 
temperature the mercury radiation produces considerable photo- 
dissociation competing with the excitation of fluorescence : after some 
time the walls of the container are covered with a deposit which is 
opaque to ultraviolet light. 

* At low benzene vapor pressures, very long exposures are necessary and 
mercury arc lamps are practically the only light sources which burn steadily 
over many hours and emit a strong line in the spectral region of the benzene bands. 

Pringsheim 10 



266 POLYATOMIC GASES AND VAPORS 

89. Simple Derivatives of Benzene. The optical properties of 
benzene derivatives in which one or several hydrogen atoms are 
substituted by other atoms or radicals are, in general, very similar 
to those of benzene vapor itself. However, the absorption bands, as 
well as the fluorescence bands, are always shifted to some extent in the 
direction of greater wavelengths, and, furthermore, the band structure, 
which in many cases is still visible in the absorption spectra, is 
frequently absent in the fluorescence spectra (Figure 92). In the most 
favorable instances (toluene, xylene, phenol), fluctuation maxima are 
superimposed on the continuous background, their spacing being, 
again, of the order of 1000 cm -1 . Even at the lowest vapor pressures 

< < < 

o o o 

o o o 



< 


< 


< 


< 


< 


< 


< 


< 


< 


< < 


4 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 2 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 


o 2 


o 


o 




CM 


ro 


•*■ 


in 


CO 


f^ 


CO 


o> o 


lA 


IO 


IO 


IO 


IO 


IO 


IO 


IO 


IO 


IO 


IO ■» 


•t 




^-Xylene 



blue-green bands 

Fig. 92. Fluorescence spectra of benzene, />-xylene, and ethyl benzene 

(Marsh). 

the conditions are not changed. This is caused not by the predominance 
of really continuous bands due to dissociation processes, but rather by 
the overlapping of ever more densely packed vibrational and rotational 
levels, and also by the fact that with increasing asymmetry of the 
whole molecule the selection rules forbidding certain transitions in 
benzene lose their strict validity. In many of these vapors a much 
greater fluorescence intensity can be obtained than in benzene vapor 
(984,985,1004). 

Aniline vapor provides an especially instructive illustration for 
most of the statements made in the last paragraph. Its absorption 
power in the first absorption band and its fluorescence intensity are 
about ten times greater than that of benzene vapor under analogous 
conditions. The absorption bands show fine structure between 3026 
and 2650A; they are followed by a series of fluctuations and, finally, 
by a continuum beginning at 2520. At high vapor pressures, the fluo- 
rescence spectrum which reaches from 2850 to 4000A is completely 
continuous with a maximum at 3150A. The mean lifetime of the 



SIMPLE DERIVATIVES OF BENZENE 



267 



f 



32 000 
3125 



I 33 



2 778 



40000 
2 500 



A 8 000 J cm." 1 
2 272 2083 XA 



excited state which can be derived from the half pressure of quenching 
by oxygen is of the order of magnitude of lO" 8 sec. 

Under excitation by light of wavelength below 2810A the 
fluorescence spectrum of aniline vapor does not show any structure 
even at a pressure of 10~ 2 mm (at room temperature) at which thermal 
equilibrium cannot be established in the excited molecules by col- 
lisions. Vartarian ascribes this behavior to the reasons discussed in 
Section 83g. The fluorescence spectrum is discontinuous, however, 
when the fluorescence is excited by the magnesium line 2937 A; the 
line coincides with a strong 
band near the longwavelength | | 

end of the absorption spectrum 
which is supposed to be the 
0' -»■ O" band of the system. 
Since under such conditions of 
excitation all excited molecules 
are in the nonvibrating state, 
the emission spectrum becomes 
a relatively simple "resonance 
spectrum." One of the prin- 
cipal spacings between band 
groups is 990 cm -1 in the 
emission spectrum and 950 
cm -1 in the absorption spec- 
trum, obviously corresponding 
to the wellknown characteristic 

frequencies of benzene. In the region between 2937 and 3027A the 
fluorescence bands coincide exactly with the absorption bands which 
are due to transitions from several levels of low vibrational energy in 
the electronic ground state. 

Addition of foreign gases does not affect the sharpness of the 
"resonance bands", but it alters the relative intensities of the 
individual bands and stimulates the appearence of a number of anti- 
Stokes bands which are also present in the absorption spectrum. 
This redistribution of vibrational energy corresponds to the establish- 
ment of thermal equilibrium in the excited state {1648,1745,1746). 

The complete fluorescence band reaching from about 3400 to 
2800A can be excited, though with small intensity, by irradiating 
saturated aniline vapor at 200° C with light of wavelength 3900A. This 
wavelength not only lies far outside of the normal absorption band of 
the vapor, but the deviation from Stokes' law very much exceeds the 
Pringsheim 10* 



Fig. 93. Spectral distribution of rela- 
tive quantum yield of aniline fluores- 
cence [Terenin, Vartanian, and Nepo- 
rent (1648)]. 

1 : vapor in absence of foreign gas. 
2: vapcr with 700 mm of NH 3 
added. 3: solution in hexane. 



268 



POLYATOMIC GASES AND VAPORS 



limit which should be expected from the available thermal energy 
The phenomenon has been explained tentatively by Duschinsky, who 
made the following assumptions: the polyatomic molecule contains, 
on the average, in each of its (3n — 6) vibrational degrees of freedom 
the thermal energy kT; absorption of light in a band near the long- 
wavelength end of the absorption spectrum transfers the molecule to 
one of the lowest vibrational levels of the excited electronic state — in 



Benzene 

Toluene 

Ethylbenzene 

p- Xylene 

Phenol 

o-Cresol 

m - Cresot 

Anisole 

Aniline 

Methylamine 

Dimethylamine 

CT - Naphthylamine 
/3-Naphthylamine 





m 


w 




































































& 


mz 


"&&>■. 




















>&& 












































**. 


m 


m 


*?», 








































ezz. 






















*? 


m 


•&>*. 
































































**> 


325= 


^ 


Vv, 
















/ 


W ■ 


^J 


0» 


0* 
















W ii 


Li 


Lii . 


*» 


















k-A 


^. 


s*>, 


7?h, 



Anthracene 
Benzopyrene 



2400 



3000 



4 200 



Fig. 94. Schematic drawing of the fluorescence 
spectra of various aromatic vapors. 



the limiting case the molecule can lose all vibrational energy. In a 
molecule of 14 atoms this would amount to 36 -kT or, at 200° C, to 
about leV. During the lifetime of the excited state, this energy is 
restored to the oscillations of the molecule by collisions and is sub- 
sequently available as additional energy for the emission process. The 
hypothesis has the shortcoming that the proposed transitions have an 
exceedingly small prqbability, but no better explanation of the pheno- 
menon and of other similar ones mentioned in Section 96 has been 
brought forward so far (331,1269). 

The fluorescence spectrum of fluorobenzene is weak and diffuse; 
the vapor of chlorobenzene is not fluorescent at all: apparently the 
light emission is completely suppressed by some competing process. 
The figures collected in Table 47, which gives only a selection of the 



SIMPLE DERIVATIVES OF BENZENE 



269 



numerous fluorescent benzene derivatives, and the schematic drawings 
of Figure 94 need no further comment. It cannot be doubted that the 



Table 47 
Fluorescence of Vapors op Aromatic Compounds 







Limits of 




Compound 


Formula 


fluorescence 
spectrum, A 


Type of bands 


Benzene 


C 6 H 6 


3100-2590 


Series of complicated band 
groups showing fine 
structure 


Toluene 


C 6 H 5 CH 3 


3400-2700 


Many narrow bands super- 
imposed on continuum 


Ethylbenzene 


C6H5C2H5 


3600-2800 


Continuum with two maxima 


Propylbenzene 


C«H 5 C 3 H 7 


3500-2850 


Weak continuum 


^-Xylene 


C 6 H 4 (CH 3 ) 2 


3850-2675 


Diffuse maxima on continu- 
ous background 


Mesitylene 


C e H 3 (CH 3 ) 3 


3800-2700 


Three maxima on continuous 
background 


Phenol 


C 6 H 6 OH 


3720-2810 


Many irregularly spaced bands 
on continuous background 


o-Cresol 


C 6 H 4 (OH) 2 


3610-2830 


Continuum 


p-Cresol 


„ 


3680-2840 


Five maxima on continuum 


Aniline 


C 6 H 5 NH 2 


4000-2850 


Fluctuations on continuum 


Fluorobenzene 


C 6 H 6 F 


2880-2640 


Four groups of bands on con- 
tinuous background 


^-Fluorotoluene 


C 6 H 4 CH 3 F 


2950-2720 


Groups of bands on continuous 
background 


o-Chlorophenol 


C 6 H 4 OHCl 


3680-2850 


Weak continuum 


Benzaldehyde 


C 6 H 6 CHO 


5000-3940 


Four band groups showing 
structure 




C 6 H 5 CH 3 CO 


4600-3900 


Three diffuse maxima 


Acetophenone 


(C 6 H 5 ) 2 


3400-2800 


Weak continuum 


Biphenyl 


(?-NH 2 C 6 H 4 ) 2 


4500-2950 


Continuum 


Benzidine 


C 6 H 5 NHC 6 H 6 


4000-2400 


Very weak continuum 


Diphenylamine 








Diphenylocta- 


C 6 H 5 — (CH = 


7000-4000 


Weak continuum with some 


tetraene 


CH) 4 _C 6 H 6 




indication of structure 


Naphthalene 


Cio"8 


4000-3080 


Many narrow bands almost 
merged in strong continuum 


Methylnaph- 








thalene 


Cio-TItC-H^ 


4500-3000 


Continuum 


Anthracene 


Ci 4 H 10 


4300-3590 


Sequence of bands (see Table 48 ) 


Naphthacene 


^16"l2 




Sequence of bands 


Benzopyrene 


^20"13 


4550-3930 


Sequence of bands (see Table 48) 


Rubrene 


Ci 6 H 8 (C 6 H 5 ) 4 


green 


? 


Octahydro- 








fluorocyclene 


C 4 sH 36 


5400-4100 


Five discrete bands 



270 POLYATOMIC GASES AND VAPORS 

fluorescence of most of these compounds is characteristic of the 
benzene ring itself, which is only slightly modified in its optical pro- 
perties by the substitutions. In addition to their ultraviolet bands, 
Marsh and his collaborators observed in the fluorescence spectra of 
many benzene derivatives a series of bands in the blue-violet (see 
Table 90, Section 138) which always have the same appearance (984, 
985,1152,1271). According to Terenin they belong to benzaldehyde, 
formed by a chemical reaction of the excited compounds, and are not 
characteristic of the benzene ring but of the carbonyl group in the 
molecule C 6 H 6 CHO. Since the absorption process takes place in the 
ultraviolet benzene band, the excitation energy must be transferred 
from one group to the other during the lifetime of the excited state 
by a kind of "internal sensitization." Similar processes will be dealt 
with later. On the other hand, aniline vapor has a second u.v. ab- 
sorption-band system which is ascribed to the NH 2 -group because of 
its analogy with the absorption spectra of other amines. The aniline 
fluorescence is not excited by light absorption in this band. 

The fluorescence bands of biphenyl are very weak and diffuse ; 
the same is true for the fluorescence bands of the diphenyl polyenes, 
while the fluorescence of these compounds in liquid solutions, and 
especially at low temperatures, shows a very definite structure 
(compare Section 134). 

90. Condensed Aromatic Hydrocarbons. The aromatic hydro- 
carbons, consisting of from two to ten and more condensed benzene 
rings, are all fluorescent in liquid solutions and many of them have 
been found to be fluorescent in the solid crystalline state. It is very 
probable that this is also the case for the vapors of these compounds, 
although only relatively few instances are actually known. It was 
rather surprising that the simplest of these hydrocarbons, naph- 
thalene, was not among them, while its fluorescence in liquid and solid 
solutions has been the subject of numerous investigations. Marsh 
obtained only a continuous emission band in the Tesla-luminescence 
spectrum of naphthalene vapor; he emphasized that it was the only 
case in which the fluorescence spectrum of the vapor showed less 
structure than that of the liquid solutions (985). However, a more 
recent report proved that by irradiating naphthalene vapor with mono- 
chromatic light of wavelenghts below 3000A, the fluorescence emission 
of a long series of narrow bands is excited; bands which are super- 
imposed between 3000 and 3340A on a strong continuum form the 
prolongation of a similar series of absorption bands ; the two sets of 
bands coincide in the overlapping region. Vapor pressure and wave- 



SPECTRA OF CONDENSED AROMATIC HYDROCARBONS 27] 

length of the primary radiation do not affect the aspect of the fluo- 
rescence spectrum (i2g2). V. Henri, who was very successful in 
investigating the spectra of polyatomic compounds, has derived a 
complete electronic energy-level scheme of naphthalene by combining 
the photo- and cathodoluminescence spectra of the vapor, of liquid 
solutions, and of the crystalline state with infrared bands of the vapor. 
Such constructions seem to lack a sound foundation, however, because 
the electronic energy levels are always strongly influenced by the 
surrounding medium, so that no conclusions can be drawn from 
apparent numerical relations between the frequency differences oc- 
curring in the spectra of the vapor and of solutions. 

Publications dealing with the fluorescence of anthracene vapor 
are much more numerous. A strong violet fluorescence is excited by 
irradiating the saturated vapor at a temperature above 100° C with 
light of wavelengths below 3700A; the spectrum consists of four 
rather diffuse bands with a spacing Jv= 1370 cm -1 . Only the first of 
these bands is resolved into three sub-bands, which coincide exactly 
with the last long-wavelength band of the absorption spectrum. From 
there the absorption spectrum continuues in the direction of smaller 
wavelengths with a series of diffuse bands. The spacing of the ab- 
sorption bands of 1380 cm -1 is nearly the same as that of the emission 
bands ; this seems to prove that the vibrational frequency responsible 
for its appearance is nearly identical in both electronic states. At a 
vapor pressure of 0.1 mm (110° C), the same fluorescence bands are 
excited by the radiation of various light sources (mercury, zinc, or 
carbon arc) as long as all wavelengths below 3100A are eliminated by 
inserting a glass plate in the path of the primary light ; a decrease of 
pressure to 0.02 mm (90° C) decreases only the intensity of the fluo- 
rescence, while the first group of the fluorescence bands is suppressed 
by self -absorption, if the pressure is raised to 1.5 mm (150° C).* Thus, 
even at the low density prevailing at the pressure of 0.02 mm, all 
molecules seem to be transferred into the same vibrational levels 
during the lifetime of the excited electronic state. This behavior may 
be due to the relatively long lifetime which F. Perrin found for 
anthracene dissolved in various viscous solvents. If his result can 
be applied to the vapor, it would not be surprising if the fluorescence 
of the vapor would be always completely depolarized, as has been 
stated in one of the papers dealing with the question. Under practically 

* This is probably the reason why, in earlier papers, the short-wavelength 
group of anthracene fluorescence bands is not mentioned (362, 996). 



272 POLYATOMIC GASES AND VAPORS 

the same experimental conditions, however, Suppe obtained a degree 
of polarization p = 33%; the reason for this discrepancy has not 
yet been cleared up (i2g2,i^gg). 

If anthracene vapor is irradiated with the cadmium line group 
near 36 12 A, which coincides with the last absorption band of the vapor, 
the fluorescence spectrum has a strikingly different aspect : the diffuse 
bands are replaced by groups of line-like narrow bands which are 
shifted with regard to the former by about 400 cm -1 in the direction 
of smaller wavelengths. The spacing between the groups is again 1370 
cm -1 , while the distance between the individual sub-bands is of the 
order of 80 cm -1 . If the vapor pressure is increased from 1 1 0° to 1 50° C , 
the structure disappears and the fluorescence spectrum recovers its 
"normal" type. Although the behavior differs in several details, the 
phenomenon is very similar to that of aniline vapor described in the 
preceding section, and it must be explained, in the main, by the same 
assumptions (i2g2). It seems reasonable to expect that also the 
fluorescence spectra of other aromatic compounds which are con- 
tinuous, in general, would exhibit the structure characteristic of their 
absorption bands, if a line coinciding with the O' -* O" band were 
used for excitation. 

Anthracene has a second absorption band system showing two 
diffuse maxima in the short-wavelength u.v. ; it corresponds to another 
electronic transition. The violet fluorescence is excited by light 
absorption in these bands at even considerably lower vapor pressures 
because of the greater absorbing power of the vapor for the short- 
wavelength u.v. radiation. Since no light emission accompanies the 
transition from the higher electronic state to the emitting state, the 
transition must correspond to a process of internal conversion. In 
such a process very numerous vibrational levels of the emitting state 
must be populated and therefore the fluorescence band is under these 
conditions quite continuous between 3600 -and 4400A. 

The fluorescence of phenanthrene, which is an isomer of anthra- 
cene, has been the subject of several publications, in which it is 
described as being very similar to that of anthracene. It is very, likely, 
however, that this fluorescence was really due to admixtures of anthra- 
cene, as shall be pointed out in a later section, while the fluorescence of 
pure phenanthrene is exclusively ultraviolet (458c). 

The only other instance of a polycyclic aromatic hydrocarbon of 
which the fluorescence spectrum has been investigated in the vapor 
state is represented by benzopyrene. The spectrum is similar to that 
of anthracene and is excited equally by the near-u.v. radiation of a 



SPECTRA OF HETEROCYCLIC COMPOUNDS ; DYES 



273 



mercury and a carbon arc. The details of the spectrum, as well as of the 
fluorescence spectrum of anthracene vapor, are listed in Table 48. The 
bands show some structure and are separated by intervals of 1400 cm -1 
(1292). 

Table 48 

Fluorescence Bands of Anthracene and Benzopyrene Vapors 

(Wavelengths of band maxima in A) 



Compound 


Wavelength of band maxima 


Anthracene 
Benzppyrene 


3595 3650 3695 
3930 


3858 
4050 4080 4150 


4074 
4262 


4300 
4320 


4520 



Only the color of the fluorescence is known for the vapors of a 
few additional compounds : dark blue for retene, orange red for naph- 
thazarine, bright blue for perylene and rubrene. At higher vapor 
pressures the fluorescence of rubrene turns into a deep green because 
of the reabsorption of the blue and violet light by the vapor.* 

91. Heterocyclic Compounds; Dyes. The number of heterocyclic 
aromatic compounds, and especially of dyestuffs, which are known 
to be fluorescent in solutions is almost unlimited. Only a few of them 
have been investigated in the vapor state. This may be due partly to 
the reasons mentioned in Section 86, but it is probable that the number 
of fluorescent vapors might easily be increased. The few examples 
which have been tested so far are listed in Table 49. While nothing is 
known about the fluorescence of acridine vapor, the acridine dye, 
acriflavine (trypaflavine), can be heated up to 350° C without being 
destroyed, its vapor showing a bright blue fluorescence when irra- 
diated with violet light. The fluorescence of the vapors of anthra- 
quinone and of indigo was mentioned by Wiedemann and Schmidt 
in 1895; the fluorescence color of the vapor of the Kodak dye, 1,4- 
diaminoanthraquinone, turns from pure green into yellow with in- 
creasing vapor pressure. Considering the results obtained by Prilesha- 
jewa with the vapors of indigo blue and indigo red, it may be doubted 
whether this change of color is exclusively caused by reabsorption. 
The fluorescence spectra of the two indigo dyes is very similar, but a 
much greater intensity is obtained with indigo blue. If the vapor of 
the dye is irradiated with light of the near u.v. (2700-3800A), the fluo- 

* Unpublished observations; this holds also for most cases mentioned in 
the following section. 



274 



POLYATOMIC GASES AND VAPORS 



rescence is violet, its spectrum extending from 2800 to 5500A; by 
unresolved white light a blue fluorescence is excited, reaching from 
3700 to 6000A. When a green filter is inserted in the path of the 
primary light, the fluorescence is yellow-green ; it becomes orange by 
inserting a yellow filter, and red when the filter is orange. This is the 
only example known, at present, in which Stokes' law is obeyed in this 
strict manner (1274,1834). 

Table 49 
Fluorescence of Vapors of Dyes 



Compound 


Fluorescence color 


Compound 


Fluorescence color 


Acriflavine 
Anthraquinone 
Diaminoanthra- 
quinone 


blue to green* 
blue 

green to yellow* 


Indigo red 
Indigo blue 


blue 
violet to redf 



* Depending on vapor pressure. 

f Depending on wavelength of exciting light. 

92. Sensitized Fluorescence of Aromatic Compounds. The fluo- 
rescence of indigo vapor is not excited by light of wavelengths between 
2700 and 2400A ; if some aniline vapor is admitted into the observation 
chamber, the violet indigo fluorescence flashes up. Since the aniline 
vapor absorbs the incident light, the indigo fluorescence is excited, 
under these conditions, as sensitized fluorescence. 

On the other hand, the excitation spectrum of aniline-vapor 
fluorescence is confined to the spectral region 2850-2500A; the zinc 
line 2500A produces only a very weak fluorescence in aniline vapor of 
0.1 mm. After an exposure of half an hour, the photographic plate is 
not appreciably blackened. In the presence o-f benzene vapor of 15 mm, 
the aniline fluorescence excited by the zinc line is so much enhanced 
that it can be photographed in several minutes. In a mixture of aniline 
and benzene vapor, the benzene fluorescence, which is easily excited 
by primary light of wavelength 2500A, is very weak, while the aniline 
fluorescence is still noticeable at a partial aniline vapor pressure of 
0.005 mm, at which it cannot be excited by light absorption in the 
long-wavelength absorption bands of aniline itself. Apparently the 
transfer of excitation energy from the benzene molecules to the 
aniline molecules has a very high efficiency (1273). 

The phenomena described in the last two paragraphs are instances 
of typical sensitized fluorescence; they are interesting in themselves, 
because they are (apart from the case of the acetone-biacetyl 



FLUORESCENCE OF METAL HALIDES 275 

fluorescence) the only instances of sensitization by polyatomic molecules 
which have been observed so far in the vapor state. It is, however, 
even more surprising that either of the two processes is reversible. It 
has already been mentioned that the aniline emission bands can be 
excited with small intensity as anti-Stokes fluorescence by irradiating 
the vapor with light of wavelengths up to 3900A. In the presence of 
indigo vapor, this anti-Stokes fluorescence is enhanced at least ten 
times. Similarly, the benzene fluorescence, which is not excited directly 
by the magnesium line 2800A, appears in the emission spectrum, 
though only with small intensity, if aniline vapor is added to the 
benzene vapor. The excitation spectra of the three vapors and the 
fluorescence bands of indigo, aniline, and benzene are so distinct that 
any mistake is quite out of the question. A satisfactory explanation 
of the mechanism by which the energy for this anti-Stokes fluorescence 
is provided has not yet been suggested. 

Another phenomenon may at least be mentioned in this con- 
nection. According to Prileshajewa, nitrogen, hydrogen, and carbon 
oxide quench selectively those parts of the fluorescence bands of the 
vapors of ethylbenzene, toluene, and aniline which are "in resonance" 
with some vibrational levels of the quenching molecules. Since the 
fluorescence bands are situated in the u.v., the quenching molecules 
must be transferred into very high vibrational levels of their electronic 
ground state, the corresponding quantum numbers v lying between 
10 and 15. It has been pointed out in another section that such pro- 
cesses are exceedingly improbable from the theoretical viewpoint, and, 
since the effects obtained by Prileshajewa are little pronounced, her 
results must be confirmed by other investigations before they can be 
taken for granted {1272). 

C. Fluorescence of Radicals Produced by Photodissociation 
of Polyatomic Molecules 

93. Metal Halides. The photodissociation of the triatomic halides 
of Hg, Cd, and of Zn is quite analogous to that of diatomic metal 
halides, discussed in Section 69. The compounds can be dissociated by 
absorption of light in several continuous bands, and the only dis- 
tinguishing feature is that one of the products of the dissociation 
process is not a metal atom but a metal halide radical, according to 
the equation: 

MeX 2 + hv -* MeX + X* or Me'X + X 



276 POLYATOMIC GASES AND VAPORS 

The wavelength of the primary light determines the excited state 
in which one of the two separating particles is found after the 
dissociation. Light absorption in the continuum of greatest wavelength 
produces, again, excited halogen atom X* in a metastable state ; if, by 
absorption of light of shorter wavelength, an excited radical Me'X 
results from the dissociation, a molecular band is emitted subsequently 
instead of an atomic line. In Table 50 all results obtained with the 
halides of mercury, cadmium, and zinc are collected: Me'X, Me"X, and 
Me" 'X denote three excited electronic states of different energy; a, 
b, c . . . are the absorption or selective excitation bands ; absorption of 
light in these bands excites the emission of the fluorescence bands 
A, B, . . The fluorescence bands consist, in most cases, of long se- 
quences of band edges or fluctuations which can be analyzed partially 
in accordance with the band theory for diatomic molecules, although 
this analysis frequently seems to be somewhat arbitrary. It is assumed 
that the lower electronic state which is reached by the emission of the 
bands B, C, and D is the ground state of the molecule MeX, because 
the spacings between the maxima in the three band systems have nearly 
the same values ; taking this for granted, the heat of dissociation for 
the process MeX 2 -+ MeX + X can be derived from the wavelength 
of the exciting light and that of the fluorescence bands. Since the latter 
is much less well defined than the wavelength of an atomic line, this 
method of determining the heat of dissociation is even less accurate 
here than it was in the case of the diatomic metal halides. 

The continuum of longest wavelength in which absorption of light 
produces the emission of a fluorescence band (e.g., C) is designated 
in the table by the corresponding small letter (e.g., c). However, the 
same fluorescence band may be excited with even greater efficiency 
by light absorption in a continuum of smaller wavelength; e.g., 
the violet fluorescence "B" of Hgl, which can be excited by irradiation 
of HgI 2 -vapor with light of wavelength 2240 (absorption band b), 
becomes much stronger if the primary radiation contains light of 
A < 1870, which is absorbed in band c (696,1152,1633-1636, 1661, 
1836-1840). 

Several additional processes occur in the photodissociation of the 
lead halides. By absorption of light in two different continua, only one 
band characteristic of the radical PbX is excited; therefore it is 
probable that the two absorption bands correspond to the two 
processes : PbX 2 + Av->PbX + X*andPb'X + X, X* representing, 
again, the halogen atom in the metastable state 2 P 1/2 . Apart from the 
PbX-bands, the X 2 -bands and a number of atomic Pb-lines appear 



FLUORESCENCE OF METAL HALIDES 



277 



in the fluorescence spectrum. Pb-lines are also observed in the ab- 
sorption spectrum of the vapors. At the temperature and vapor 
pressure of the experiments (given in parentheses in Table 50), the 
vapors are dissociated thermally to a certain degree. However, since 
the intensities of the X 2 -bands and of the atomic lines are quadratic or 
even cubic functions of the primary light intensity, two or more 
individual absorption processes are contributing to their excitation, 
which, therefore, cannot be a case of normal sensitized fluorescence. 
The mechanism of the energy transfer from the excited PbX 2 -molecules 



Table 50 

Absorption and Fluorescence Bands of Polyatomic Metal Halides 

(a, b, c . . . absorption bands; A, B, C . . . corresponding fluorescence 

bands; wavelengths in A) 



Products of 
dissociation 


Band 
symbol 


Hgl, 


HgBr, 


HgCl, 


Cdl 8 


CdBr 2 


Znl, 


ZnCl 2 


MeX + X* 
Me'X + X 

Me"X + X 

Me'"X+ X 

? 


a 

b 
B 

c 

c 

d 
D 

e 


2600 

2240 

4450- 

3500 

1820 

3100- 

2800 

1730 

2800- 

2650 

1600 


2240 

1950 

5040- 

3500 

1700 

2900- 

2700 

1600 

2700- 

2500 

2700- 
2500 


1850 

1810 

5660- 

3400 


2620 

2230 

5670- 

5085 

2070 

3500- 

3250 

1820 

? 


? 

1970 
7000- 

? 


2200 

1960 

6000- 

5300 


? 

1750 

5600- 

4900 

1600 

3800- 

2850f 






Pbl 2 (450°,0.3 mm) 


PbBr, (250°,! mm) 


PbCl 2 (500°,2 mm) 


PbX + X* 
Pb'X + X 


b 

b' 

B 

x z 


2326 

2020 

5000-4000 

(12 broad bands) 

5600-5350 

(structure uncertain) 


2230 

2080 

4950-4433 

(22 band edges) 

5600-5050 
(13 band edges) 


2050 

1950 

4921-4098 

(69 band edges) 

5258-4941 

(48 band edges) 



f Three different excited states are ascribed, in a more complete analysis of the 
ZnCl-spectrum, to the bands listed here as fluorescence band C; if this is correct, 
the representation given in this table probably is too simple also for the other 
halides. 



278 POLYATOMIC GASES AND VAPORS 

to the X 2 -molecules and the Pb-atoms has not yet found a satisfactory 
explanation. This holds also for the excitation of the mercury resonance 
line 2537A, which is always present in the fluorescence when Hgl 2 is 
photodissociated. 

The yellow-green iodine bands are emitted if the vapor of stannic 
iodide at a pressure of 110 mm (saturated at 60° C)> is superheated 
to temperatures above 350° C and irradiated with light of wavelengths 
between 2500 and 2150A. In this case, the impossibility of a direct 
excitation of free I 2 -molecules has been proved experimentally: no 
fluorescence is produced by illuminating the vessel with green light, 
which is most effective in stimulating the visible iodine fluorescence 
{1103). Free iodine, which is actually produced by the photodissoci- 
ation, must be frozen out carefully in order to prevent quenching of the 
fluorescence. The intensity of the I 2 -fluorescence is proportional to the 
intensity of the primary light and, therefore, cannot be caused by a 
recombination process of the type I + I* -* I 2 *. On the other hand, 
the emission of the iodine bands is not observed at temperatures 
below 320° C and is continuously enhanced by raising the temperature 
to 550°, the limit reached in the experiments for technical reasons. In 
tin tetraiodide, the iodine atoms are not grouped in pairs, but form 
a tetrahedron symmetrically surrounding the central tin atom. Only if, 
at high temperatures, the amplitudes of the oscillations become 
sufficiently large, can two of them approach each other so closely 
that they can be separated in a single act from the parent molecule 
as an exited iodine molecule. Terenin calls this process "inner 
recombination in the photodissociation of a polyatomic molecule." 
Some of the I 2 -bands emitted under these conditions are anomalously 
enhanced, irrespective of the wavelength of the exciting light; 
according to Terenin, the abnormal intensity distribution is caused 
by a selective transfer of vibrational energy from the excited iodine 
molecule to the remainder of the original compound, Snl 2 (61,1103, 
1647). 

A yellow-green fluorescence which has been observed in super- 
heated vapor of Bil 3 has been ascribed by Terenin to the analogous 
process Bil 3 + h v ->■ Bil + I 2 *, notwithstanding the fact that the 
fluorescence band is quite continuous. f Simultaneously, a number of 
atomic Bi-lines are emitted which may be due either to a secondary 
photodissociation: Bil + hv-+Bi* + I, or to a direct excitation of 
Bi -atoms present in the vapor (1101). 

t Therefore, the band had been ascribed previously to an excited molecule 
Bil„. 



FLUORESCENCE OF OTHER POLYATOMIC MOLECULES 279 

If the vapor of Gal 3 saturated at 300° C is irradiated with light 
of wavelengths below 208OA, the atomic gallium lines 4033 and 41 72 A 
appear in the fluorescence spectrum. A weak band at 3915A, which is 
excited by the radiation from a carbon arc, is ascribed by Petrowa to 
the undissociated molecule Gal 3> while a much stronger yellow 
luminescence, which is excited only by light of wavelengths shorter 
than 1800 A, is supposed to result from the photodissociation of the 
compound into Ga'I + I 2 . The origin of a greenish fluorescence excited 
at 230° C by short-wavelength u.v. in the vapor of GaBr 3 has not been 
determined (1230,1818). 

The emission of the CuCl-bands due to the photodissociation of 
Cu 2 CL; by light of wavelengths below2370A has already been mentioned 
in Section 61. Butkow's and Terenin's earlier experiments were re- 
peated by Terrien, who obtained essentially the same results and 
succeeded no better than the Russian investigators in explaining the 
energy relations of the processes involved. If he illuminated the vapor 
simultaneously with u.v. light (A < 2370A) and the lines of the Cu 
resonance doublet 3248/74A, the resonance lines reappeared in the 
fluorescence spectrum in addition to the CuCl-bands. The intensity of 
the doublet dropped to 1 j i if the total primary intensity was reduced to 
1 I 2 by means of a wire-gauze filter. Irradiation with the lines of the 
doublet alone was ineffective. Hence, it seems that the copper atoms 
are separated from Cu 2 Cl 2 or CuCl-molecules by the absorption of 
ultraviolet light and are subsequently excited by absorption of the 
atomic lines while still in the gas phase, before they are precipitated 
(191,1649). 

Finally, a visible fluorescence is observed when the vapors of 
CH 3 HgI and CH 3 HgBr are illuminated by the light of strong sparks ; 
the fluorescence is violet in the first, and blue in the second case. The 
color of the emission and the spectra are identical with those obtained 
in the vapors of Hgl 2 and HgBr 2 . However, the fluorescence appears at 
much lower temperatures in the vapors of the organic compounds and 
the spectral range of the exciting light is different from that of the 
mercury halides. It is certain, therefore, that the primary process is 
a photodissociation of the compounds according to the equation: 
CH 3 HgX + Av->CH 3 + HgX* (1646). 

94. Other Polyatomic Molecules. Terenin and his collaborators 
have observed the fluorescence of radicals which were produced by 
the irradiation of various polyatomic molecules with the Schumann 
u.v. of a hydrogen discharge lamp. By inserting very thin quartz 
plates and fluorite plates into the path of the exciting light they were 



280 



POLYATOMIC GASES AND VAPORS 



able to determine the short-wavelength limit of the processes qualita- 
tively. From this limiting wavelength A„ and the fluorescence 
wavelength X F , they calculated the electronic energy E of the excited 
radicals and the heat of dissociation D of the compounds (681,683, 
684,1104,1638). 

Table 51 

Photodissociation of Molecules Containing the Radicals 
OH, CN, NH„ and NO 



Compound 


Products of 
dissociation 


D + Ein 


eV 


^,inA 


Xp in A 


H 2 


H + OH* 


5 + 4 


= 9 


1370 


3062 


CH3OH 


CH 3 + OH* 


3.9 -f 4 


= 7.9 


1560 


3062 


C„H 5 OH 


C 2 H 5 + OH* 


3.9 + 4 


= 7.9 


1560 


3062 


HCOOH 


HCO + OH* 


3.9 + 4.6 


= 7.9 


1560 


3062 


HCOOH 


HCO* + OH 


3.9 + 3.6 


= 7.5 


1630 


3400 


CH3COOH 


CH3CO + OH* 


3.9 + 4 


= 7.9 


1560 


3062 


CH 3 CN 


CH 3 + CN* 


4.57 + 3.18 


= 7.75 


1600 


3863 


ICN 


I + CN* 








3863 


C 2 N 2 


CN + CN* 








3863 


NH 3 


H + NH a * 


5.1 + 2.4 


= 7.5 


1630 


5000 


N 2 H 4 


NH., + NH a * 


5.3 + 2.4 


= 7.7 


1580 


5000 


N a O 


N + NO* 


4.1 + 5.6 


= 9.7 


1280 


4000 



The OH-band at 3062A, corresponding to the vibrational quan- 
tum numbers 0' -> 0", is by far the strongest in all spectra in which 
the OH-radical is the carrier of the fluorescence and shows abnormally 
high rotational quantum numbers; the band at 2811 A (l'->0") is 
much weaker, while the band at 3428A (0'-*- 1") is noticeable only 
in the photodissociation spectrum of formic acid. In addition to the 
OH-bands, the fluorescence of formic acid contains a sequence of 
diffuse bands very similar to those of formaldehyde. However, the 
two sets of bands do not exactly coincide, and Terenin suggests that 
the new bands might belong to the radical HCO. 

The band sequence with Av = (0' -> 0", 1' -> 1", 2' -> 2") be- 
tween 3883 and 3862A has the greatest intensity in the CN-fluorescence 
following the photodissociation of various cyanogen compounds ; the 
sequence Av = + 1 (0' -* V, 1' -► 2", 2' -* 3") between 4216 and 
4181A is much weaker and the sequence Av = — 1 (1' -»■ 0", 2' -> 1") 
between 3590 and 3586A is only just noticeable. 

The emission bands of N~H 2 exhibit a great number of narrow and 
closely spaced sub-bands; they are designated, in general as a-bands 



FLUORESCENCE OF OTHER POLYATOMIC MOLECULES 281 

of ammonia. The fluorescence has about the same intensity when the 
radical NH 2 is produced by dissociation of ammonia or hydrazine 
vapor; it is rather weak in the vapor of methylamine. 

N 2 has a number of continuous absorption bands between 3000 
and 1400A. The products of the dissociation processes corresponding 
to these bands are O- and N-atoms and NO- or N 2 -molecules in the 
ground state or in metastable states, so that no light emission follows 
the dissociation. By absorption of light in a very strong band at 1280A, 
however, the N 2 0-molecules are split into a nitrogen atom in the ground 
state and an NO-molecule in the excited state B^IJ. From there the 
molecules can return to the ground state with emission of the so-called 
jS-band of NO, which reaches from 5270 to 2185A; the great length of 
the band system is caused by the fact that the potential curve of the 
excited state, with an excitation energy of 5.6 eV, has its minimum at 
a much greater internuclear distance than the potential curve of the 
ground state. In Sen Gupta's experiments, only the long-wavelength 
part of the band was obtained by means of a glass spectrograph ; the 
intensity distribution in this part of the system was normal, with the 
highest intensity in the bands at 4589, 4041, and 3800A. Light of 
wavelengths greater than 1800A, which would suffice for directly 
exciting the /J-bands in NO-gas, was ineffective and thus it could be 
proved that the emission was really caused by the photodissociation 
ofN 2 0(^ 9 3). 

The fluorescence of the OH-radicals is strongly quenched by 
addition of CO and H 2 ; the influence of foreign gases in reducing the 
abnormally hig"h rotational energy in the OH- and CN-bands has been 
dealt with in Section 67. The fluorescence of CN is quenched by N 2 
more effectively in the 0'->-0" band than in the 1 '-»■ 1" band. For the 
NH 2 -fluorescence, nitrogen, carbon monoxide, and argon have about 
the same quenching efficiency. Most of these quenching processes 
seem to be caused by induced predissociation, but Terenin assumes 
that the OH-fhiorescence is quenched by chemical reactions between 
the excited OH-radicals and hydrogen or carbon monoxide molecules. 



PART II 

Fluorescence and Phosphorescence 
of Condensed Systems 



CHAPTER IV 
GENERAL SURVEY 

A. Nature of Luminescent Substances 

95. Conditions for Occurrence of Photoluminescence. Unperturbed 
fluorescence of gases and vapors is noted only at lowest pressures. At 
pressures at which collisions of excited molecules become sufficiently 
probable, either the secondary radiation is changed in frequency, or 
its intensity is weakened or even completely quenched. Polyatomic 
molecules seem to be less sensitive to quenching by collisions, in 
general, than monatomic vapors. In condensed states (pure liquid or 
solid, liquid or solid solution) the ability to fluoresce is lost, however, 
even in the majority of polyatomic compounds. The reasons for the 
absence of fluorescence due to the interaction of excited molecules 
with other molecules are, in principle, the same in condensed systems 
as in vapors : inducedpredissociation, chemical reactions, and "internal 
conversion." It is easily understood that the first of these processes 
has a greater chance of realization in condensed systems, where the 
excited molecules are in a constant state of collision.* In most 
instances no chemical reactions are produced by the absorption of 
light, and, especially if the nature of the surrounding molecules (of 
the solvent, for instance) has no marked influence on the optical 
properties of the absorbing substance, the re-emission of radiation 
must be suppressed by the third type of process (424). 

The probability of internal conversion is greatly enhanced in 
condensed systems for two reasons. If, in a polyatomic vapor, the 
electronic excitation energy of an isolated molecule is converted to 
high vibrational energy of the electronic ground state, the inverse 
process must occur after some time. This fluctuation of energy from 
one form to the other may be repeated more than once, but as long as 
no collision takes place, the absorbed energy must eventually be re- 
emitted as radiation. Whenever a molecule has acquired a high 

* It has already been pointed out that, on the other hand, the probability 
of spontaneous predissociation can be reduced by the stabilizing effect of 
collisions (see Section 83). 

285 



286 CONDENSED SYSTEMS 

vibrational energy in a condensed system, this energy is almost 
immediately dissipated into thermal agitation of the surrounding 
medium and is never restored to the initially excited molecule. 
Also a molecule in a condensed system, especially in a solution, can 
never be treated as an isolated entity: in nearly every case it forms 
some sort of complex with surrounding molecules, e.g., of the solvent. 
Many metal ions exhibit, in aqueous solutions, absorption bands of 
much lower frequencies than those of the resonance lines in the vapor 
state and these may be due at least partially to electronic transitions 
between the dissolved molecules and the solvation envelope by which 
they are surrounded. In other instances the influence of the solvents on 
the absorption spectra of the dissolved molecules is relatively small, 
but none the less an interaction between the latter and the solvation 
envelope takes place and can greatly influence the fluorescence yield. 

Since the existence of narrow absorption bands proves the corre- 
sponding electronic transitions to be well protected against pertur- 
bations from outside, one might assume that molecules exhibiting such 
bands should have a greater chance to be fluorescent than others. This 
is correct up to a point: among compounds with narrow absorption 
bands the number of fluorescing substances is relatively great, al- 
though fluorescence is by no means a general property of such com- 
pounds. For instance, the chromium alums and the uranous salts are 
not fluorescent. On the other hand, the absorption bands of many 
strongly fluorescent dye solutions are no less diffuse and broad than 
those of nonfluorescent dyes. Very small changes in the constitution of 
a molecule can have a great influence on the probability of internal 
conversion and, thus, on the occurrence or nonoccurrence of fluo- 
rescence without appreciably affecting the power of absorption. 

96. Most Important Types of Luminescent Substances. If photo- 
luminescence is a characteristic property of a compound as such, the 
molecules of this compound must be fluorescent under various con- 
ditions — for instance, when the compound is in the crystalline state, 
in a liquid solution, and in the vapor state. Practically all molecules 
which are photoluminescent in condensed states are more or less 
complex. The only exceptions are the positive ions of some rare-earth 
metals, the optical properties of which are so little perturbed by the 
surrounding medium that, even in crystals or in aqueous solutions, 
they behave almost like the atoms of a vapor. Among the complex 
inorganic molecules the positive ions UO++ are, with few exceptions, 
fluorescent in crystalline uranyl salts and in liquid solutions of such 
salts. A few other metallic ions (Tl + , Pb ++ , and Sn ++ ) are able, in 



ENERGY TRANSFER FROM ABSORBING TO EMITTING MECHANISM 287 

aqueous solutions, to form complexes which can be excited to fluo- 
rescence (521,522,617,1304). In addition the cyanoplatinites are 
to be mentioned and, finally, some derivatives of siloxene which, 
owing to their ring structure, have much in common with aromatic 
compounds. It is doubtful whether the tungstates, molybdates, and 
some similar salts should be included in this class for, although many 
crystals containing these ions are strongly photoluminescent without 
being appreciably contaminated by an impurity, nothing is known 
about their fluorescence in other than the crystalline state. Thus, they 
may be classified as belonging to the mineral crystal phosphors. 

Although only a relatively small number of inorganic compounds 
must be considered here, organic chemistry provides an almost un- 
bounded wealth of examples, especially in the class of aromatic and 
polycyclic compounds', beginning with benzene and reaching to the 
most highly complex dyestuffs. 

No less numerous are the substances belonging to the last main 
class of materials which are luminescent in the solid state. They are 
called "crystal phosphors."* As indicated by this designation, it is no 
longer an individual molecule which is luminescent by itself. The 
ability to re-emit absorbed radiation as light is intimately related to 
the condition that the molecules form a part of a crystal lattice ; in 
most cases the luminescence is due to the incorporation of minute 
impurities into the "base material" of the crystal. 

In general, only fluorescence is observed in liquids and most 
frequently it is a fluorescence of very short duration. Very weak 
phosphorescence has been obtained, however, with some liquid dye 
solutions (136,745^270). Although a strong afterglow of considerable 
duration is observed with many solids (glasses as well as crystals), 
phosphorescence lasting many hours, and even days, after the end of 
the excitation seems to be a specific property of crystal phosphors 
"activated" by impurities. 

97. Energy Transfer from the Absorbing to the Emitting Mecha- 
nism. In the isolated complex molecules of a vapor, radiant energy 
can be absorbed in one part of a molecule and pass into another 
part the characteristic fluorescence of which is subsequently emitted. 
If collisions occur, the electronic energy of an excited molecule can be 
transferred to the colliding molecule with subsequent emission of 
"sensitized fluorescence." Similar processes may take place in con- 

* Many organic compounds are luminescent in the crystalline state, and 
so are uranyl salts and the platinous cyanides, but in these cases the crystalline 
form is not an essential condition for the occurrence of luminescence. 



288 CONDENSED SYSTEMS 

densed systems. The first type is observed at its best with certain 
complex rare-earth salts in liquid solutions. 

The excitation and fluorescence spectra of crystalline or dissolved 
inorganic europium salts (nitrates, sulfates, etc.) are confined to 
several groups of narrow lines, and the fluorescence intensity which 
can be attained is weak. Organic salts of europium, such as the salicyl- 
aldehyde or the benzoyl acetonate, have strong continuous absorption 
bands between 3200 and 4400A, and the characteristic europium line- 
fluorescence is excited with great intensity if the salt is irradiated with 
light of any wavelength between these limits. It is certain that the 
broad absorption bands which appear also in the absorption spectra of 
the organic compounds containing no rare earth are not connected 
with an electronic transition within the europium ion. The excitation 
of the internal electronic system of Eu+++ is caused by light absorption 
in another part of the complex molecule. The efficiency of the energy 
transfer seems to depend a great deal upon the nature of the bond 
between the rare-earth ion and the absorbing radical. It is best in the 
purely covalent, benzene-soluble benzoyl acetonate, less good in the 
picrate, and completely missing in europium cyanoplatinite crystals 
with their purely ionic bonds (1816). 

Probability of the energy transfer must also depend, however, on 
still other conditions, for the same compounds which provide the 
strongest europium fluorescence are quite inefficient with terbium. On 
the other hand, the green terbium line-fluorescence is excited with 
great brilliancy by light absorption in the u.v. bands of terbium 
acetoacetanilide, while the corresponding europium compound is very 
slightly fluorescent. 

The converse effect has been obtained by Tomaschek. The 
excitation of the blue-violet fluorescence characteristic of organic 
acids by the Hg-lines at 3 1 30A is greatly enhanced in the gadolinium 
salts of these acids (for instance, gadolinium salicylate) which in 
addition to the normal absorption bands of the acids show the 
typical absorption lines of the trivalent gadolinium ion in the vicinity 
of 3130A (Section 140). The violet fluorescence of the europium salts 
of the same organic acids is only very slightly excited by the Hg-lines 
at 3 130 A, while the fluorescence of the gadolinium and of the 
europium salts is excited with equal rather low intensity by the Hg- 
lines at 3650A which are not selectively absorbed by either of the 
rare-earth ions (i6g8c) . 

While the phenomena described in the last paragraphs may be 
designated as internally sensitized fluorescence, the experimental 



ENERGY TRANSFER FROM ABSORBING TO EMITTING MECHANISM 289 

proofs for the occurrence of externally sensitized fluorescence in 
liquid solutions are rather unconvincing. 

In crystals still other means of energy transfer from an absorbing 
to an emitting center must be taken under consideration: "internal 
photoelectric effecfand "exciton migration."These might be regarded 
as belonging to the category of energy transfer within a complex 
molecule, insofar as a crystal can be treated as a huge polyatomic 
molecule. In the first instance, an electron is completely detached by 
light absorption from its normal location and, transporting a certain 
amount of energy, it travels across the crystal lattice until it excites 
light emission at another point within the crystal. Exciton migration 
is a purely quantum-mechanical resonance phenomenon ; in a certain 
way it is similar to the diffusion of a resonance light quantum in the 
"imprisoned radiation" of mercury vapor. However, the total time 
during which the photon remains within the vapor as imprisoned 
radiation is the sum of the individual lifetimes of the single excited 
atoms, while, in a crystal, the total lifetime corresponding to exciton 
migration becomes shorter in the same ratio as the number of identical 
crystal elements which take part in the resonance process becomes 
larger. The excitation energy does not belong to an individual element 
at any moment, but simultaneously to all of them; the probability of 
emission increases correspondingly, and if the crystal is homogeneous 
it is not possible to determine whether the absorbing and the emitting 
centers are the same or not. If the crystal contains an impurity with a 
characteristic emission band of its own, light absorption may be due 
to the base lattice, through which the energy travels as an exciton 
until it reaches the impurity center where, finally, the radiation is 
emitted. 

Both phenomena are of special importance for crystal phosphors. 
As these differ in many respects from other classes of luminescent liq- 
uids and solids, it seems advisable to treat their properties separately. 
But photoconductivity and exciton migration can also occur in 
luminescent crystals which do not belong to the class of "crystal 
phosphors" and, thus, they should be mentioned here (14^,428, 1803). 
Leaving the crystal phosphors aside, the properties more or less 
common to all other photoluminescent solids and liquids are collected 
in the following sections, while in later chapters the principal classes 
of fluorescent substances are treated. This division of the material, 
although leading to some repetition or overlapping, seems to be the 
best way by which a more general understanding of the phenomena 
can be attained. The crystal phosphors are dealt with in the last chapter. 



290 CONDENSED SYSTEMS 

B. Course of the Emission Process 

98. Fluorescence and Phosphorescence. It has already been men- 
tioned in the introductory chapter that, in the present state of 
knowledge and experimental technique, the duration of the emission 
process does not supply an unequivocal method of distinction between 
fluorescence and phosphorescence. J. Becquerel held the opinion that 
no essential difference really existed between the two kinds of photo- 
luminescence, and that there was a continuous transition from the 
first to the second. As we know now, the situation is complicated by 
the fact that typical fluorescence is not inconsistent with a relatively 
long afterglow. For phenomena of this kind, F. Perrin introduced the 
term "fluorescence of long duration," which, for the sake of brevity, 
will be replaced here by "slow fluorescence" (A,2j2,X22i). 

An instance in which all possible luminescence processes can be 
observed and which corresponds to the energy-level diagram of Figure 
1 is provided by mercury vapor which is excited, at room temperature 
and in the presence of nitrogen, by the absorption of the resonance line 
2537A. Some of the excited atoms re-emit the line as fluorescence 
within the normal lifetime (10 -7 sec) of the state 6 3 P X ; other atoms are 
transferred by collisions with nitrogen molecules into the metastable 
state 6 3 .P . Some of these emit the forbidden line'2655A and thus 
return to the ground state by a relatively improbable transition which 
has a much longer decay period and must be designated as slow 
fluorescence. Other 6 3 P -atoms are brought back to the 3 P 1 -state by 
collisions with. nitrogen molecules of sufficient energy, and the final 
process is, once more, emission of the resonance line. The duration of 
this afterglow depends primarily on the frequency of collisions with 
sufficient energy (in other words, on the temperature) and is a typical 
phosphorescence. 

For the complex molecules which have to be considered in these 
paragraphs, the energy levels and the corresponding transition proba- 
bilities are almost never as well known as they are in the example of 
the mercury atom. Nevertheless, it is possible also to give here general 
criteria for the discrimination between fluorescence and phosphores- 
cence. Becquerel's' hypothesis seemed, at first, to be corroborated by 
an experimental result. Wiedemann and Schmidt found that while 
liquid dye solutions showed only fluorescence with no measurable 
afterglow, a phosphorescence could be observed and its duration could 
be increased if the viscosity of the solution was increased by the 



FLUORESCENCE AND PHOSPHORESCENCE 291 

addition of gelatin (1454,1835). A similar afterglow could be observed 
when the dye was dissolved in various solids such as sugar, benzoic 
acid, albumen, etc. Later, however, Vavilov and Levshin proved that 
there was no gradual increase of the duration of luminescence but 
that in the solid solutions the fluorescence retained the same short 
lifetime, of the order of magnitude of 5- 10 -9 sec, and that a second 
process of much longer lifetime was superimposed on this fluorescence 
(1766). Boudin was the first to observe a phosphorescence lasting 
about 10~ 3 sec in a diluted eosin solution in glycerol free of oxygen 
which was placed in a Becquerel phosphoroscope. Kautsky obtained 
similar results with aqueous and alcoholic solutions of eosin, erythrosin, 
rose bengale, phloxin, and porphyrin ; the relatively strong afterglow 
of chlorophyll could be observed only when the dye was dissolved in 
pure isoamylamine (1 36, 46g, 7 50,1453,1454). 

In every one of these cases the fluorescence and the phosphor- 
escence are excited by light of the same wavelength and their emission 
spectra are identical : the light absorption leads to, and the emission 
starts from, the same excited level. It is obvious that the relatively 
stable state to which some of the excited molecules are transferred and 
which causes the appearance of phosphorescence is characteristic of 
the molecule itself; the phosphorescence is weak or completely miss- 
ing in liquid solutions only because the probability of some sort of 
quenching process is much greater in this case. When phosphor- 
escence occurs, the intensity of the luminescence drops to a much 
lower level at the moment when the primary radiation is cut off; from 
there on, it decays continuously to zero. 

If an afterglow can be observed in a phosphoroscope or even 
without such an instrument, and if the intensity curve shows no 
discontinuous break immediately after the end of the excitation, the 
afterglow is not phosphorescence but a slow fluorescence [corre- 
sponding to the emission of the forbidden line by the Hg (6 3 P )- 
atoms]. If this afterglow lasts only a few thousandths of a second or 
less, the bands corresponding to the same electronic transition are 
observable also in the absorption spectrum, and the slow fluorescence 
can be excited "directly" by light absorption in these bands (272 
1218,1227,1767). 

Many organic substances can be excited to emit a slow fluo- 
rescence different in color from their normal fluorescence and lasting 
several seconds. In general no band corresponding to the forbidden 
electronic transition which produces this slow fluorescence is found in 
the absorption spectrum; emission is excited by light absorption in 



292 CONDENSED SYSTEMS 

the normal absorption bands of the substance, exactly as emission 
of the forbidden Hg-line is excited by absorption of the mercury 
resonance line and a subsequent transferof theatoms to the metastable 
state: it is an "indirectly excited" slow fluorescence. It has already 
been stated that the visible slow fluorescence of Eu+++and Tb+++ 
which can be excited directly is excited indirectly, with much greater 
intensity, in certain complex organic compounds (1816). 

The long lifetimes of the states M from which phosphorescence 
and indirectly excited slow fluorescence originate need not be due [as 
in the case of Hg(6 3 P )], or at least may not be due exclusively, to 
electronic selection rules according to which certain transitions are 
forbidden or, rather, extremely improbable . Existence of longlived high- 
energy modifications of polyatomic molecules can also be explained 
by applying the Franck-Condon principle and by assuming that the 
atomic nuclei have an equilibrium configuration in state M which does 
not correspond to any configuration occurring in the electronic ground 
state. Under these conditions, a radiating spontaneous transition 
from M to N has an exceedingly small probability. Franck and 
Livingston, therefore, call the state M a tautomeric modification of 
the molecule. With a less specific designation, which may be applied 
also to the analogous phenomenon in crystal phosphors all states 
which owe their long life to the Franck-Condon principle will be 
classified as "quasi-stable," in contradistinction to those which are 
"metastable" because of an electronic selection rule (424). 

The duration of a fluorescence process is essentially independent 
of external conditions insofar as this duration is determined by internal 
transition probabilities. If the mean life t of an excited state is short- 
ened by a quenching process which might depend on the temperature 
this is, according to Equation (8), (compare Section 4, page 6) always 
accompanied by a proportional decrease in the total luminescence 
yield. Apart from such secondary effects, the temperature has no 
influence on the duration of fluorescence. As a matter of fact the after- 
glow of the uranyl salts or of the slow fluorescence bands of dyestuffs 
is very nearly the same at room temperature as at liquid-air tempera- 
ture (g27a,i22j,i302). On the other hand, it follows from the energy- 
level diagram of Figure 1 that the duration of a real phosphorescence is 
fundamentally a function of temperature, since the energy deficiency 
F — M = e must be provided by thermal fluctuations. The lower 
the temperature, the longer is the average time interval elapsing 
before the necessary energy is supplied to M. Below a certain tempera- 
ture the return from M to F will practically not occur at all, while the 



DECAY CURVES 293 

passage from N to F by light absorption and the transition from, F 
to M is not impeded. 

Thus, the phosphorescence is excited and "frozen in." If the 
temperature is subsequently raised, the absorbed energy is set free 
and re-emitted without new excitation as a brilliant flash. This phe- 
nomenon was' discovered by Dewar when he immersed barium 
cyanoplatinite* in liquid air {283). Even if the platinite is kept after 
excitation in the dark at low temperature for an hour or more, a bright 
light emission takes place when the liquid air is removed. Similar 
phenomena occur in the phosphorescence of solid dye solutions, though 
with smaller efficiency. The most brilliant examples of "frozen-in" 
phosphorescence are found in certain crystal phosphors. All so-called 
thermoluminescence is nothing but phosphorescence which already 
is frozen in at room temperature. 

99. Decay Curves. All emission processes treated in this chapter, 
normal and slow fluorescence as well as phosphorescence, are mono- 
molecular (first-order) processes. Hence, according to theoretical 
expectation, their decay curves should all be simple exponentials : 

/ = Itf-at, with a = 1/t (60) 

From fluorometric measurements and other more indirect methods, 
the fluorescence of liquid dye solutions is known to have a lifetime 
usually not exceeding 5- 10~~ 9 sec. The shape of the decay curve during 
so short a period has not yet been determined by direct experiments. 
However, the assumption of an exponential decay of the fluorescence 
of dye solutions is supported by the fact that calculations based on 
this hypothesis yield identical values for the lifetimes of excited dye 
molecules when widely differing shutter frequencies are used for ob- 
taining the fluorometer curves, from which the T-values are derived 
(compare Figure 4) (1623). Another result of fluorometric measure- 
ments, which was obtained by Cram and later confirmed by Thumer- 
man, must be mentioned in this connection. Fluorometer curves 
corresponding to the fluorescence of various dye solutions at low 
temperatures could be interpreted only by supposing that a dark 
interval of the order of magnitude of 10 -7 sec occurred between the 
end of the excitation and the beginning of the emission, while the 
latter proceeded from there on with the normal decay period of 5- 10 - ' 
sec {243,1709). The interpretation of several earlier experiments which 
seemed to prove the existence of a dark interval between the end 

* At room temperature, this compound shows only a short-lived fluo- 
rescence. 



294 



CONDENSED SYSTEMS 



of the excitation and the beginning of the emission in fluorescing 
solutions were based on erroneous assumptions concerning the methods 
used in these experiments (464,525,638,1884). Cram's and Thumer- 
man's papers do not seem to contain any fallacies of this kind, but 
no theoretical interpretation of their unexpected results has been 
found so far (Compare Section 78). 

For slower fluorescence processes a direct observation of the decay 
is possible and, in all cases in which measurements were made, the 
results were in satisfactory agreement with an exponential decay. 

Nichols and Merritt, to whom we are indebted for much important 
research on the fluorescence of uranyl salts, were of the opinion that 
this luminescence originated from a bimolecular reaction and that its 
intensity after the end of the excitation should, therefore, be repre- 
sented as a function of time by an equation of the type : 



cr s 



(61) 



From their experiments they derived for every uranyl salt several (in 
most instances, three) different values of the constant C for different 
intervals of time t, and so the curve representing 7 _i as a function of t 
was a broken line consisting of three straight branches (Figure 95). 




4.0 & 



3.2 



ZA 



0.002 sec 



Fig. 95. Decay of fluorescence of 
uranyl salts at intensities of the 
exciting radiation varying from 
2.8 to 51.0 (in arbitrary units) 
(Nichols and Merritt). 




0.8 



24 32 / x 10 



Fig. 96. The values of Figure 95 

in a plot of log I versus t [ Vavilov 

and Levshin {1767)]. 



Vavilov and Levshin showed, however, that all results published by 
Nichols and Merritt, as well as a great number of new observations of 



DECAY CURVES 



295 



2.0 



1.5 



1.0 



0.5 



their own, were represented without exception as straight lines on log I 
versus i! diagrams, in accordance with Equation (60) (Figure 96) (H,ni3, 
1116,1767). 

The same has been proved by various authors for the phosphor- 
escence and for the slow fluorescence of solid dyestuff solutions, 
platinum cyanides, canary glass, and other luminescent compounds 
with values of t larger than 10 -4 
sec (Figure 97). Minor deviations 
from strictly logarithmic decay 
curves which were occasionally ob- 
served probably can be ascribed to 
secondary effects {4^,915,9270,, 
930,1302,1428,1773). s 

For instance, if, in a solid j? 
solution with a luminescence yield 
less than 100 %, the solvent mole- 
cules surrounding the individual 
molecules of the luminescent com- 
pound do not have identical 
configurations, the excited mole- 
cules may have unequal proba- 
bilities of transferring their exci- 
tation energy to the solvent. 
Thus they would have slightly 
different mean life times and the 
decay curve would correspond 
to the superposition of numerous 
exponentials with slightly different exponents. 

As mentioned in the foregoing section, the coefficient a in Equa- 
tion (60) is a function of temperature for phosphorescence processes. 
In the first approximation the relation between a and the absolute 
temperature T is also exponential: 

a = se- e l kT 





















V 


^s^C 




a\ 


t \ 


' 


1 



12 3 sec. 

Fig. 97. Decay of the luminescence 
of trypaflavine adsorbed on silica 

gel (Pringsheim and Vogels) . 

a : green phosphorescence at 

+ 39°C. b: the same at — 18°. 

c : orange slow fluorescence 
at — 180° C. 



or log a = b + c-T x 



(62) 



where s = F — M or the heat of activation of the phosphorescence- 
process, s is nearly constant but varies slightly with the temperature- 
it determines the probability with which the process occurs when the 
energy e is provided by thermal fluctuations. 

The decay of a simple band whether fluorescence or phosphores- 
cence, is always uniform for all parts of the band. This has been proved by 
direct observation for the slow fluorescence of uranyl salts and rare- 



296 CONDENSED SYSTEMS 

earth ions, and for the fluorescence and phosphorescence of dyes in 
solid solutions ; it has been proved by indirect methods for the short- 
lived fluorescence of liquid dye solutions. In every instance where the 
color of the luminescence varies during the period of the afterglow, 
it could be shown that two emission bands of different spectral com- 
position and with different lifetimes were superimposed. An example is 
the green phosphorescence band and the yellow band of slow fluo- 
rescence emitted by trypaflavine in solid solution at — 40° C {927a, 
1302). 

Any light emission which is excited by light absorption must 
have a certain period of growth or ' 'induction" corresponding inversely 
to the decay period. With a long-lasting constant irradiation the 
luminescence reaches a limiting or equilibrium value I when the num- 
ber of molecules excited per second by light absorption is equal to the 
number deactivated by emission : 

dnjdt = A — ■ an = 0; I = an — A; a = 1/t (63) 

Absorbed energy A and emitted energy / are measured in quantum 
units, and no quenching processes of any kind are assumed to exist in 
this simple treatment. 

In analogy to the mean lifetime t at the end of which the inten- 
sity has dropped from I to I = e~ 1 I after the termination of the 
excitation, the mean induction period & can be defined as the time 
elapsed from the beginning of the excitation until the luminescence 
has attained the intensity: 

J = (1 — l/e)I (64a) 

If the luminescence is due to the same electronic transition as the 
absorption and both have the same transition probability (an assump- 
tion which is valid for practically all directly excited fluorescence 
processes), t and & are equal, irrespective of the absolute value of t . 
This follows from the integration of Equation (63) for dnjdt > 0: 

n = n (1 — e-^) for t = r a = & (64b) 

If, on the other hand, the duration of the luminescence depends par- 
tially on transition probabilities which have no influence on the ab- 
sorption process, as in phosphorescence and indirectly excited slow 
fluorescence, the mean induction period can never be longer than the 
mean decay period, but it can be much shorter. Under these conditions, 
t and & are no longer connected by a definite relation. Temperature 
determines the duration of phosphorescence because it determines the 



LUMINESCENCE INTENSITY AND "LIGHT SUM" 297 

transition probability from M to F, but it has no influence on the 
absorption process. If the intensity of the exciting irradiation is kept 
constant, a decrease in temperature increases the number of molecules 
which remain in the quasi-stable state; eventually, practically all 
molecules have been transferred into this state" when equilibrium is 
reached. The phosphor is then "fully excited "or "saturated." Greater 
intensity of the exciting light produces saturation within a shorter 
time, while this leaves the decay period of the phosphorescence un- 
altered. Similar considerations are valid for indirectly excited slow 
fluorescence. 

The existence of an induction period was discovered by Becquerel 
in luminescence processes which are now classified as slow fluorescence. 
The phenomenon is easily observed in the slow fluorescence of organic 
compounds at low temperatures (for instance, Kowalski's ' 'progressive 
phosphorescence"; compare Section 136) and in the phosphorescence 
of many crystal phosphors (815). 

100. Luminescence Intensity and "Light Sum" L. Under the 
conditions stated in the last section, according to which the periods of 
growth and decay of luminescence are equal, the relative number of 
excited molecules always remains small compared to the total number 
of unexcited molecules, even if the primary radiation has a very high 
intensity. Therefore, the fluorescence intensity is strictly proportional 
to the intensity of the exciting light over the widest obtainable range 
(582). This is no longer true if, in the course of a phosphorescence 
excitation process, a relatively great number of molecules is trans- 
ferred into a quasi-stable state M. Under these conditions, the phos- 
phorescence intensity reached at the end of the excitation process 
tends toward its saturation value I m . A further increase of the primary 
intensity has no appreciable influence on this value. Figure 98 shows 
the phosphorescence intensity of fluorescein dissolved in vitrified boric 
acid at 18° C as a function of the strength of the primary radiation : if 
the intensity of the exciting light is reduced to one-half of its maximum 
value, the phosphorescence decreases by only about 12%. Similar 
curves were obtained for the slow fluorescence of the same solid 
solution at — 185° C [930). 

For any kind of fluorescence, regardless of its duration and its 
mode of excitation, the intensity of the secondary radiation is a direct 
measure of the number of excited molecules present at the moment of 
observation, according to Equation (63), in which constant a depends 
only on the nature of the luminescent molecule. On the other hand, the 
intensity of a phosphorescence can be very small or even zero at the 



298 



CONDENSED SYSTEMS 



end of the excitation period in a fully excited phosphor. Hence, the 
number of excited molecules present at a given moment is no longer 
proportional to the actual intensity of luminescence but to the total 






40 



™ 20 40 60 80 too 

5 INTENSITY OF EXCITING LIGHT 

Fig. 98. Intensity of the phosphorescence of 

fluorescein in boric acid as a function of the 

exciting radiation at 18° C (Lewis, Lipkins, 

and Magel). 

number of light quanta the substance is still able to emit without new 
excitation, or to the "light sum" L stored in the phosphor: 



L t = I dt ot I = — dL/dt and L = /„ / e~^dt = I r 



(65) 



If a simple exponential decay is assumed for /, L is also an exponential : 

L = Ipe-* (66) 

If t is known, I and L can be derived from the measurement of I 
at any given moment after the end of the excitation. As long as t 
is constant, I and L are proportional to / at any given time t, and in 
order to find, for instance, the relative change of I or L with varying 
intensities of the primary light it is sufficient always- to measure I at 
the same time t after the end of excitation under the varying conditions 
of irradiation. 

If the intensity of the primary radiation is far below the saturation 
value,* I is equal to A [Equation (63)] as soon as the equilibrium 
state is reached and according to Equation (65) the light sum or the 
total energy stored in a phosphor at a given intensity of primary 
radiation increases proportionally with r. If experimental results 

* This condition is fulfilled in almost all cases of afterglow not exceeding 
a few seconds. 



BAND WIDTH, STOKES* LAW, FRANCK-CONDON PRINCIPLE 299 

disagree with this conclusion, some kind of quenching process must 
compete with the luminescence emission. In the other limiting case, 
when saturation is reached either because the exciting radiation is 
extremely strong or because the lifetime t is very long, L has always 
the same value at the end of the excitation period, while I decreases 
with increasing t — for instance, when the temperature is lowered. 

In a saturated phosphor, L is proportional to the total yield Q 
even in the presence of some quenching process, while 7 , being a 
function of t, is not directly connected with Q. If, on the other hand, 
the phosphor is far from being saturated, I is proportional to Q, 
regardless of the value of t, while L would increase with an increase 
of t according to Equation (66). (In the case of saturation, I would 
decrease with decreasing temperature at a constant value of Q; far 
below saturation, the luminescence intensity is always I = QA after 
equilibrium is reached). 

C. Emission, Absorption, and Excitation Spectra 

101. Band Width, Stokes' Law, and the Franck-Condon Principle. 

The energy levels of a luminescent molecule are influenced in two 
different ways by the continuous and fluctuating interaction with the 
surrounding medium. Under this influence the energy of a level is not 
sharply determined, but varies at every instant for differently located 
molecules and varies with time for every individual molecule. The 
broadening of the energy levels is due to the electronic rather than to 
the vibrational part of the total energy, since the Raman lines due to 
intramolecular vibrations are nearly as narrow in liquids as in vapors. 
Equally sharp fluorescence lines are very infrequent in condensed 
media ; they occur exclusively in crystals at low temperatures. As a 
second consequence of the continuous energy exchange with the sur- 
rounding medium, no vibrational energy transferred to a molecule by 
the absorption process can be retained by the molecule during the 
period elapsing before the re-emission takes place. Therefore, the 
emission process always originates from one of the lowest vibrational 
levels of the excited molecule. 

Lenard was probably the first to ascribe the great width of the 
bands in the emission spectra of crystal phosphors to the fluctuation 
of the molecular fields. The problem of the band width and of the 
spectral displacement of the fluorescence bands with respect to the 
absorption bands has been treated by Jablonski on the basis of the 



300 



CONDENSED SYSTEMS 



Franck-Condon principle. His considerations were essentially the 
same as those used for polyatomic vapors at high pressures. The energy 
of an individual state, however, no longer depends only on the 
electronic and vibrational energy of the molecule itself, but is affected 
by the configuration of the surrounding molecules which may have 
different equilibrium distributions if the electronic state of the mole- 
cule is changed. AH these parameters are now included in the represen- 
tation of the potential energy by "configuration potential curves." 
The latter admittedly give a rather incomplete picture of the real 
situation, but are easier to visualize than polydimensional potential 
surfaces. In general, the minima of the curves representing the ground 
state and the excited state do not have the same abscissas; due to 
zero-point energy and thermal fluctuations, the molecules do not 
occupy these minima but oscillate about them with a Maxwellian 
distribution. Because of this distribution in the ground state, the ab- 
sorption band has an appreciable width and an approximatively 
symmetrical intensity distribution around a center, which corresponds 
to the vertical transition from the minimum of the lower curve to the 
upper curve. After re-establishment of thermal equilibrium in the 
excited state, which corresponds again to a Maxwellian distribution, 
the return to the ground state produces an emission band of about the 
same width and shape which were characteristic of the absorption 
band and with a center of gravity which must always be shifted in the 

direction of longer wavelengths (Figure 99) 

(659)- 

The intensity distribution within the 
emission band is independent of the exact 
wavelength of the exciting light {656). 
Only if thermal equilibrium should not be 
re-established during the lifetime of the 
excited state would the energy- distribution 
in the luminescence band be more or less 
influenced by the wavelength of the exciting 
radiation. Experiments which seemed to 
show the existence of such an effect were 
performed by Starkiewicz on dye solutions 
in water-free glycerol and were explained 
by the slower energy exchange in a highly 
viscous medium. However, these experi- 
ments are not very conclusive (1555). [A 
similar effect was described by Gudden 




Absorption 



Fig. 99. Potential curves 
for fluorescence in a con- 
densed system 
(Jablonski). 



BAND WIDTH, STOKES* LAW, FRANCK-CONDON PRINCIPLE 301 

in the fluorescence of certain crystal phosphors and was explained by 
the same assumption (536).] 

Corresponding to the "anti-Stokes" terms in the resonance 
spectra of diatomic vapors, small departures from the strict form of 
Stokes' law also occur in the fluorescence of condensed systems. The 
question of the possibility of exciting fluorescence by light of wave- 
lengths longer than that of the secondary radiation has been 
the subject of much discussion; eventually it was proved that the 
whole fluorescence band is emitted even if the luminescence is excited 
by a line which lies inside the range of the emission band. This means 
only that the absorption (or excitation) band and the fluorescence 
band overlap. Theoretically it is explained by the same assumption as 
every anti-Stokes fluorescence, namely, that a part of the excitation 
energy is supplied by the thermal energy of the surrounding medium. 
The center of the absorption band, however, is always displaced in 
the direction of shorter wavelengths with respect to the emission 
band (814). 

The effect of temperature on the appearance of anti-Stokes 
fluorescence has been demonstrated very convincingly by Wood, who 
excited the fluorescence of an aqueous uranin solution by light of the 
longest wavelength capable of stimulating fluorescence at room tem- 
perature. The intensity of the fluorescence was enhanced considerably 
by heating the solution to 100° C; this is not due to an increase in 
fluorescence yield, but to an increase in absorption at the long- 
wavelength end of the absorption band. At higher temperatures a 
greater fraction of the molecules in the electronic ground state populate 
the higher vibrational levels and thus absorb light of greater wave- 
length. The gain in anti-Stokes fluorescence exceeds even the apparent 
gain in fluorescence intensity, because simultaneously and for analo- 
gous reasons the emission band stretches farther in the direction of 
shorter wavelengths (1892). 

If the lowest points in the potential curves N and F of Fig. 99 
have widely different abscissas, a broad interval separates the long- 
wavelength end of the absorption band and the short-wavelength 
end of the emission band. Otherwise the two bands overlap, and, if the 
secondary radiation has to travel a considerable distance before 
emerging from the fluorescent medium, a part of the fluorescence light 
is reabsorbed in this medium. An apparent displacement of the center 
of the emission band can be produced thereby, but such an effect is by 
no means able to explain the "Stokes shift," as was assumed by 
J. Stark ; without the independent existence of the Stokes shift, a band 

Pringsheim 11 



302 



CONDENSED SYSTEMS 



reversal and not a displacement of the center of the band would be the 
result of reabsorption. 

In order to obtain the real spectral intensity distribution within 
a fluorescence band, either the emission by an infinitely thin layer or 
by a very dilute solution must be investigated, or the observations 
must be extrapolated to these limiting values by measuring the 
spectral distribution of the absorbing power of the fluorescing medium 
and integrating over the radiation coming from different depths. 



_ 


- 67 °A 


/V 67» 




_ 


i t 






- 


/ Azo° \ 




V 


- 






^* 




*£r 1 




X. ^ 




a/Q >(■ 


\ 


>0^ 


-°^ 


r Fl. // 


V Abs. 


''No n. 




1 -^"\ 


1 > 


1 1 >o 



16000 



18000 



20 000 



Fig. 100a. Mirror symmetry of absorption and 

fluorescence bands. 

Rhodamine 6 G in ethanol (Levshin). 



102. So-called Mirror Symmetry. The diagram of Figure 99 ex- 
plains the general analogy between the absorption and emission bands 
and the fact that changes in temperature affect the two types of bands 
in a similar way. It also determines the limits beyond which the fre- 
quently quoted, so-called law of mirror symmetry loses its validity. 
This law was first stated by Levshin on purely empirical grounds. 
It contends that if the intensities of an absorption band and of the 
corresponding fluorescence band are plotted as functions of the 
frequency,* the two curves are symmetrical with respect to a fre- 
quency v lying halfway between the peaks of the two bands (Figures 
100« and b) (gi2~gi4). 

In the simple case of a diatomic molecule such a symmetry exists 
only if the shapes of the potential curves of the combining states are 

* The intensities are measured in quanta (I/hv) and the peak of the 
emission curve is given the same value as the peak of the absorption curve. 



SO-CALLED MIRROR SYMMETRY 



303 



the same and if, consequently, the vibrational frequencies cog and ai' 
as well as their anharmonicities w"x" and co'x' are identical in both 
electronic states. Under these conditions the center of symmetry 
corresponds to the 0"-<— >0' band which coincides with all other tran- 
sitions Av = and has the greatest intensity in both the absorption 
and the emission spectrum. If, on the other hand the potential curve 
of the excited state is appreciably shifted with respect to that of the 
ground state, the transition 0"< — >0' has a vanishing probability and 




1 22001 cm -i v 

4700 4 500 A X 



Fig. 1006. Mirror symmetry ol absorption and fluorescence 

bands. 

Triphenylmethyl in pentane-ether-ethanol mixture 

at — 190° C (Lewis, Lipkin, and Magel). 



the two spectra no longer overlap. At the same time the vibrational 
frequencies and the values of the cox's differ in the two electronic 
states, and, if to" is larger than to', the absorption spectrum (repre- 
sented by the progression v" = 0, v' = 0, 1, 2 . . .) is compressed into 
a smaller frequency range than the fluorescence spectrum (v' = 0, 
v" = 0, 1 , 2 . . .) : the symmetry law does not hold. 

These considerations, which are strictly correct only for diatomic 
molecules, can be applied also to polyatomic molecules with several 
vibrational frequencies (o lt to 2 , a> 3 , etc., if a progression of one of these 
frequencies (e.g., aij) is the predominant feature of their spectra. The 
spectra of benzene and of the uranyl salts, which have been quoted 
by Levshin as examples of the mirror symmetry, belong to this class. 
In the emission spectra of both, the spacings between the main band 
groups are appreciably larger than those in the absorption spectra. 
Moreover, the intensity distribution in the absorption and fluorescence 



304 CONDENSED SYSTEMS 

spectra of the uranyl salts differs widely. While the fluorescence 
spectrum consists of bands due to a single electronic transition, the 
corresponding band system in the absorption spectrum is overlapped 
by bands with slightly different spacings which are due to transitions 
to several higher electronic states ; eventually these overlapping band 
systems merge into a continuum which probably is connected with a 
photodissociation process (Fig. 101) (1288, I28g). 

The conditions are essentially different if the first band in the 





Fig. 101. Absorption and flu- 
orescence spectra of uranyl 
sulfate in aqueous solution 
(Pringsheim) . 

a : absorption in layers of 

increasing thickness. 
b: fluorescence. 

absorption spectrum and the fluorescence band of a polyatomic mole- 
cule do not correspond to a progression of the type assumed above, 
but to a single vibrational transition &[ = -> w[ = 1 and coj = -»• 
coj = 1, respectively, on which vibrational frequencies <o 2 , w 3 . . . are 
superimposed. The electronic excitation may affect only the frequency, 
w x , while the internuclear bonds which determine the other vi- 
brational frequencies remain practically unaltered. The band group 
is then represented in the absorption spectrum by the frequencies 
toj, coj + w 2 , cj' x + u> 3 , . . . and in the fluorescence spectrum by the 
frequencies w v co[ — u> 2 , a>l — w s , ... (or 2co 1; 2^ + w 2 , etc., ac- 
cording to the relative displacement of the two potential curves) and 
the center of symmetry is no longer the missing band 0*-<-->-0' but a 
point halfway between the two bands, which are separated by the 
frequency gap w^ + o}[ (compare Section 83, g). 

An example of this kind seems to be represented by the ab- 
sorption and fluorescence spectra of the radical triphenyl methyl 
(Figure 1006). Pauling pointed out that the frequency differences 



SO-CALLED MIRROR SYMMETRY 



305 



occurring between the individual band maxima of these spectra were 
in fair agreement with Raman frequencies of other compounds con- 
taining the same bonds. Another case of a similar nature is discussed 
more fully in Section 134 (g32,i20i). 

Levshin has collected a great many examples of dye solutions for 
which his symmetry postulate holds even if the absorption and fluo- 
rescence bands undergo appreciable changes by variation of tempera- 
ture, choice of solvent, etc. (Figure 100a). In these examples, both 
bands are influenced in the same way by the changing conditions 

(CI- 
TABLE 52 

Wavelengths of the Absorption and Fluorescence Band Peaks 
of Merocyanine Dyes in Different Solvents 



Solvent 


« = 


= l 


n = 


= 2 


n 


= 3 


Abs. 


Fl. 


Abs. 


Fl. 


Abs. 


Fl. 


Cyclohexane . . 
Pyridine + H 2 . . 


4920 
5240 
5400 


5480 
5590 
5627 


5380 
6000 
6310 


6330 
6440 
6510 


5700 
6340 
7100 


(6470) 
7650 
7830 



For other types of dyes, the spectral shift of the absorption band 
can be much larger than the shift of the emission band"; thus, the 
gap between absorption and emission bands is altered. Table 52 shows 
this effect for three merocyanines, as given by Brooker; n indicates 
the number of (CH = CH) groups present in the compound Similar 
observations referring to the diphenylpolyenes will be mentioned in 
Section 134. Such a behavior can be ex- 
plained by the assumption that, while the 
ground state and the equilibrium position 
of the excited state are less influenced by 
the nature of the solvent, the slope of the 
upper potential curve is appreciably 
changed. If A x and A 2 represent the po- 
tential curves of the excited state in two 
solvents, the absorption transitions a-+b x 
and a -*■ b 2 correspond to different frequ- 




Fig. 102. Potential curves 
showing relative shift of 
absorption band by inter- 
action with the solvent. 



encies, while the emission frequency of the 
transition c ->■ d remains unaltered (Figure 
102). 

The intensity distribution within a 
simple absorption or emission band depends, in the first place, on 
Pringsheim 11* 



306 



CONDENSED SYSTEMS 



the distribution of vibrational energy in the absorbing or the emitting 
molecules, and, in the second place, on the fluctuations in the con- 
figuration of the surrounding medium. Since both follow the laws of 
statistics the spectral intensity-distribution curve of each band 
should also have the shape of a Gaussian error curve as was pointed 
out by Lenard with respect to the phosphorescence bands of crystal 
phosphors. The nearly symmetrical bell shape is lost if two adjacent 
bands, which may correspond to different electronic transitions, 

overlap. It may be doubtful, 
however, whether it is cor- 
rect to analyze every inten- 
sity curve which is not 
exactly bell-shaped as the 
superposition of two or 
several Gaussian curves, as 
has been done by Lenard 
and his school. 

103. Fluorescence In- 
tensity as a Function of 
Absorbed Energy. Although, 



20 



16 



12 



- 




r y\ 




- 


1 / 


A yj \ 




- 


/A 

lot 
I / 

M * 

r/ 


/ \ * 

/ \ * 


V 




*#w 


*V\ 




- O" 


1 7 

i i 


■ i 


1 1 



4700 



5000 



5300 



5600 



5900 A j n g enera j ( ever y fluores- 

Fig. 103. Absorption, excitation, and emis- C ence band is associated 
sion spectra of eosin in aqueous solution wkh an absorption band 

(Nichols- and Merritt). r 



I. absorption 
II. fluorescence spectrum 

III. noncorrected excitation spectrum 

IV. excitation spectrum reduced to equal 
amounts of absorbed energy. 



corresponding to the same 
electronic transition, the 
excitation of the fluores- 
cence of condensed systems 
is never restricted to this 
narrow spectral region. The introduction of the term "excita- 
tion spectrum" or "excitation distribution" (translating Lenard's 
"Erregungsverteilung"), which is frequently mentioned in older pu- 
blications, was due to the fact that the fortuitous superposition of the 
spectral energy distribution in the primary radiation and in the ab- 
sorption spectrum of the fluorescent substance was not taken into 
account.* If these are determined by quantitative measurements and 
if the fluorescent intensities are reduced to the values corresponding 
to equal absorbed energies, all spectral selectivity in the exciting power 
of the primary light disappears. 

* In Ms first important paper on fluorescence, Stokes states that fluo- 
rescence is excited only by light which is absorbed by the fluorescent substance 
{1585)- 



FLUORESCENCE INTENSITY AND ABSORBED ENERGY 



307 



Nichols and Merritt were the first to prove this; in Figure 103, 
curves / and II represent absorption and fluorescence bands, res- 
pectively, curve III the relative intensities of the fluorescence excited 
by light of various wavelengths transmitted through a monochro- 
mator, and curve IV the specific exciting power as a function of the 
wavelength of the primary radiation {1018,1123-1125). Nichols and 
Merritt's results were later corroborated and enlarged in two respects. 
Valentiner and Roessiger found that the efficiency of the exciting 
radiation decreased rapidly as soon as the wavelength of the primary 
light became larger than the wavelength corresponding to the peak 



100 








1 1 




- 






/ 'Abs. 


80 


0' 




'" r ~~~"-TkJ 


Q .* 60 

t 40 








A 


20 




I 1 1 1 




/'Abs. \ \ 


24 


00 


3000 


4000 


5000 



Fig. 104. Quantum yield of the fluores- 
cence of an aqueous solution of fluorescein 
sodium as a function of the exciting 
wavelength (after Vavilov). 



of the fluorescence band. For an aqueous fluorescein solution with the 
maximum of the emission band at 5250A, the relative efficiency of 
excitation by the line Hg 5461 A was ten times smaller than the 
efficiency of excitation by Hg 4358A. Such a turning point may be 
indicated by the last point of curve IV and in Figure 103 (1730,1731). 
Vavilov, who extended the measurements over a wider spectral range 
of exciting radiation down to 2500A, showed that the relative efficiency 
increased linearly with the wavelength or inversely with the frequency 
v of the exciting light, the coefficient of proportionality being equal 
to Planck's constant h. Hence, the fluorescence intensity is propor- 
tional to the number of absorbed light quanta irrespective of the 
wavelength of the exciting light (Figure 104) (1747,1748,1750). This 
constancy of the quantum efficiency for exciting light of all wave- 
lengths smaller than that of the emission band has since been proved 
for numerous substances (for instance, esculin, sodium salicylate, 



308 CONDENSED SYSTEMS 

chlorophyll, and uranyl salts). Most of these investigations were 
undertaken in order to test the possibility of applying "integrating 
fluorescent screens" to u.v. heterochromatic photometry (16,140,220, 

27i,3i5,579,58i). 

The steep drop of efficiency in the region of greater wavelengths 
which has been observed by Valentiner has also been confirmed in 
several instances. This phenomenon cannot be interpreted without 
introducing new assumptions. According to the potential curves of 
Fig. 99, the long-wavelength branch of the absorption band is ascribed 
to molecules having a relatively high vibrational energy in the 
electronic ground state. As the number of these molecules is small, the 
absorption intensity is weak in this part of the band. But there is no 
reason why these molecules, once they are lifted by light absorption 
into the excited state, should have a smaller probability of subsequent 
fluorescence emission than any other excited molecules. The fluo- 
rescence intensity excited by a given energy of incident light will be 
relatively small, but the quantum efficiency should still be the same. 
It can be assumed however, that the wings of the absorption bands 
are due mainly to molecules which are strongly perturbed by the 
interaction with adjacent molecules. According to Franck and 
Rabinowitch, this interaction can last considerably longer than a 
single collision in the gas phase, because of the so-called cage effect, 
and, thus, internal conversion can be made probable, inhibiting the 
eventual fluorescence re-emission of the absorbed energy. Jablonski 
has suggested that the decrease in fluorescence yield at greater wave- 
lengths may be due to the fact that transitions from the ground state N 
to a quasi-stable state M contribute a considerable fraction to the 
absorption in the long-wavelength part of the normal absorption band. 
It will be shown in Section 136 that the transition from N to M has a 
probability almost 10 8 times smaller than that of the transition from 
the ground state to the fluorescent state F. On the other hand, the 
absorption coefficient of the dye solution at the wavelength at which 
the yield begins to decline in the curve of Figure 104 is still about one 
per cent of the absorption coefficient at the center of the absorption 
band. Therefore, Jablonski's hypothesis does not seem to provide an 
adequate interpretation of Figure 104 (compare Section 120) (660, 
679). 

Figure 103 and 104 show that the excitation of fluorescence is not 
restricted to the absorption band which corresponds to the same 
electronic transition, but reaches with unaltered quantum efficiency 
not only into the adjoining region of small absorption, which might 



FLUORESCENCE INTENSITY AND ABSORBED ENERGY 



309 



still be regarded as the tail of this band, but into a second absorption 
band of much shorter wavelength which corresponds to the transition 
into a higher electronic state (N-+G) (compare Figure 129). Under 
these conditions, the emission of the normal fluorescence band F->iV 
can be only the second part of a stepwise return into the ground state . 
Since the emission of a second fluorescence band corresponding to the 
transition G -> F has never been observed, this transition must be due 
to an internal conversion. It is rather astonishing that the quantum 
efficiency of the fluorescence is the same as when F is reached directly 
by light absorption; it must be assumed that all molecules raised to 




3400 



Fig. 105. Absorption and excitation spectra of 

magnesium platinocyanide in aqueous solution 

(Khvostikov). 

a: absorption coefficient in arbitrary units 

b : same with ordinate enlarged 30 times 

c: fluorescence yield 

Straight line calculated according to Ein- 
stein's law. 



the state G pass into a high vibrational level of F without any losses 
due to a direct return to the ground state. It should be remembered 
that the same behavior was observed with respect to the excitation 
of fluorescence in anthracene vapor. 

While, in general, the fluorescence yield is independent of the 
wavelength of the exciting light, aqueous solutions of cyanoplatinites 
show a different behavior. Their absorption spectrum consist- of a band 
in the near ultraviolet with peak at 2780A and long-wave limit at 
3500A, and of a second much stronger and narrower band at 2500A. 
Fluorescence is excited with an energy yield decreasing linearly with 
the wavelength as long as the primary light is absorbed in the first 
band, but the yield drops sharply to zero at the boundary of the second 



310 CONDENSED SYSTEMS 

band. By light absorption in this band the molecules must be raised to 
a state from which fluorescence emission occurs neither directly nor 
indirectly (Figure 105) {775). 

Not only the fluorescence yield but also the energy distribution 
in the fluorescence spectrum is independent of the wavelength of the 
exciting light for practically all fluorescent compounds (aromatic 
hydrocarbons, dye solutions, rare-earth salts, cyanoplatinites etc.) 
{656). Substances in which different emission bands are excited 
by light of different wavelengths are exceptional. The fluorescence of 
meldola blue in aqueous solution, for instance, is orange when excited 
by radiation corresponding to its main absorption band (5500-6 100A) 
and greenish under excitation by blue-violet light. It is probable that 
these two different fluorescence bands belong to two constituents of 
the commercial dye. The same explanation may be applied to 
the change of the fluorescence spectrum which Andant observed when 
he excited solid alkaloids with light of different wavelengths. In the 
afterglow of malachite green and crystal violet dissolved in glycerol 
at — 100° C, G. N. Lewis obtained the emission of a red band when 
the solution was irradiated with light absorbed in the visible absorption 
bands of the dyes, while a green emission band appeared only under 
irradiation with near u.v. Lewis ascribed the latter to a pseudo-isomer 
formed by the addition of a solvent molecule of the type ROH, of 
which OR goes to the central C-atom and H to one of the nitrogens. 
As a matter of fact, the same green emission bands were obtained in 
the luminescence spectra of the carbinols of malachite green and 
crystal violet dissolved in a mixture of ether, pentane, and ethanol at 
— 183° C* {927a). 

If the influence of various parameters, such as concentration, 
temperature, quenching by foreign molecules, etc., on the fluorescence 
yield is to be investigated, it is sufficient, in general, for the reasons 
stated in the preceding paragraph, to limit the measurements to a 
part of the emission band which is most convenient because of better 
visibility, easy separation from the exciting radiation by complementa- 
ry niters, absence of reabsorption by the fluorescing medium, etc. The 
total fluorescence intensity can be derived from these measurements 
once the intensity distribution in the fluorescence band has been 
determined under favorable experimental conditions. 

* Although not mentioned explicitly, it must be supposed that the red 
bands are missing in the emission spectra of the carbinols in glycerol at — 100° C; 
at the temperature of liquid air they would have disappeared also from the 
luminescence spectra of the normal dyes (see Section 136). 



ABSORPTION BY MOLECULES IN THE EXCITED STATE 3 1 1 

104. Absorption by Molecules in the Excited State. An excited 
mercury atom has absorption lines differing from those of the atom 
in the ground state. Broad absorption bands which originate from 
the groundstate N and an excited state F of a complex molecule in a 
condensed system may more or less overlap, so that light of the same 
frequency can be absorbed by molecules in either of these two states. 
Under any circumstances, however, light absorption by a molecule 
in state N or in state F transfers the molecule to a different upper 
state: either from N to F, or from F to a higher electronic level G. In 
general, the two bands N -> F and F-+G will belong to different 
spectral regions. 

In most fluorescence processes the number of excited molecules 
which are to be found at any moment in the state F remains small 
compared to the number of molecules in the ground state, and, there- 
fore, the absorption bands corresponding to transitions F ->■ G remain 
below the limit of observability, while the intensity of the absorption 
band N -*■ F is apparently constant. No trace of a change in the 
absorption coefficient of a dye solution could be obtained by Vavilov 
and Levshin, even when they used the very highest attainable inten- 
sities provided by a condensed spark as their source of excitation 
and, simultaneously, -as background for their absorption measurements. 
When they replaced the dye solution by a canary glass with an appreci- 
ably slower decay of luminescence, they found an effect just outside 
the limit of probable error. It must be emphasized, however, that the 
lifetime of the excited state does not affect the relative number of 
excited atoms which are in equilibrium with a given primary radiation, 
as long as absorption and emission correspond to the same electronic 
transition, since a longer lifetime is compensated by weaker ab- 
sorption (1766).* 

The conditions are much more favorable if, as in the experiments 
performed by Lewis and his co-workers, a slow fluorescence is ex- 
cited indirectly by light absorption in a strong absorption band. 
This, for instance, is the case when, at low temperatures, dye molecules 
in solid solution pass from the directly excited state F to a quasi-stable 
state M from which they return to the ground state under emission of 
a slow fluorescence. The normal absorption spectrum of fluorescein in 
boric acid is represented by curve 1 of Figure 106; curve 2 of the figure 
shows the absorption spectrum of the same solution irradiated with 

* In canary glass the uranyl fluorescence may, perhaps, be excited in- 
directly by light absorption not taking place in the uranyl ions but in some 
other component of the glass. 



312 



CONDENSED SYSTEMS 



the very strong light of a high -pressure mercury arc at — 95° C. The 
maximum of curve 1 at 4365A has become much lower in curve 2, 
while an absorption band apparently consisting of two overlapping 
parts with maxima at 5050 and 6500A is greatly enhanced. It belongs, 
beyond doubt, to the excited state M, its small but measurable 
intensity in curve 1 being due to the weak radiation used for the 
absorption measurements. Figure 107 represents the decrease in 
absorption band 1 and the increase in absorption band 2 with in- 
creasing irradiation. It is to be noted that illumination of the excited 
molecules with light absorbed in band 2 has no influence on the fluo- 







- 


/ V 


- 


/ V 


— ' — f H 


i 



8000 



6000 
WAVELENGTH, A 



4000 



Fig. 106. Absorption spectrum of 
fluorescein in boric acid [Lewis, 
Lipkin, and Magel (930)]. 
1 : in ground state N. 2 : par- 
tially excited quasi-stable 
state M. 



0.8 - 



o 

z 



2 0.4 



^•tt._. 2 



-° O 

? 40 80 

J INTENSITY OF EXCITING LIGHT 

Fig. 107. Effect of intensity of 
exciting light on the absorp- 
tion of fluorescein in boric acid 
[Lewis, Lipkin, and Magel 
(930)]. 
1 : 6500A. 2 : 4360A. 



rescence process ; all molecules raised from M by light absorption into 
some higher levels Lor K return to M from where the emission process 
originates. Whereas this behavior differs from that of certain crystal 
phosphors, it corresponds to the observations which were described 
in the preceding section. It has been pointed out that all molecules 
of fluorescent organic molecules which are raised by light absorption 
in a short-wavelength absorption band to a higher electronic state are 
transferred from there by radiationless transitions to the excited state 
F and not directly to the ground state N (930). 

During the first decade of this century the existence of a so-called 
fluorescence absorption was the subject of much discussion and of a 
good deal of experimental research. The concept was based on an 
erroneous analogy with Kirchhoff's and Bunsen's well-known ob- 



ABSORPTION BY MOLECULES IN THE EXCITED STATES 313 

servation that a sodium flame absorbs the same lines (the D-lines) 
which it emits. This observations lead to the inference that the light 
absorption was due to the emitting atoms. However, sodium vapor 
absorbs the D-lines also at temperatures at which no emission occurs, 
and, as a matter of fact, the "emitting atoms," or the atoms in the 
excited state, are the only ones which have no part in the absorption 
process. The experiments in search of a new absorption band of fluo- 
rescence substances, which was assumed to appear during the emission of 
fluorescence and to coincide exactly with the fluorescence band, seemed 
partially to prove and partially to disprove the hypothesis, but even- 
tually all apparently favorable results could be shown to be caused 
by experimental error. Perhaps the most convincing proof of the non- 
existence of fluorescence absorption was brought forward by J. 
Becquerel. The index of refraction and, thus, the absorption coefficient 
of ruby in the neighborhood of its exceedingly sharp fluorescence lines 
is not altered by a fraction of a per cent when the crystal is excited 
to strong fluorescence (84,1018,1126,1865). 

D. Luminescence Yield as a Function of 
Experimental Conditions 

105. Definition of Yield and Methods of Measuring It. The fluo- 
rescence yield has been denned for gases as the ratio of the total 
intensity emitted by a volume of gas in a certain time to the total 
light intensity absorbed by that volume in the same time. This 
definition remains correct for condensed systems as long as it is 
applied to states of equilibrium during the period of excitation. For 
phosphorescence processes it is not difficult to integrate the energy 
emitted after the end of the excitation, but it is not possible, in general, 
to determine which part of the absorbed energy has been immediately 
re-emitted as fluorescence and which part has been stored in the 
"phosphorescence centers," since both processes are excited by light 
of the same wavelengths. 

If a part of the incident light is absorbed by molecules which do 
not contribute to the fluorescence — for instance, molecules of the 
solvent or of a second dissolved substance — this must, if possible, 
be taken into account in calculating the fluorescence yield. 

The light intensities are measured either in energy units such as 
ergs or watt seconds or by the number of quanta comprising the 
radiation. In the first instance, the "energy yield" 0, and, in the 



314 CONDENSED SYSTEMS 

second, the "quantum efficiency" Q, is obtained. The relation between 
and Q is given by the equation: Q = (X a /X e )$, where X a and X e are 
the wavelengths of the absorbed and emitted radiation, respectively. 
Q is always smaller than, or, in the limiting case of X a = X e (resonance 
radiation), equal to $>. When the terms efficiency or yield are used 
without qualification in the following paragraphs, they always refer 
to the quantum yield. 

The same processes which completely inhibit the appearance of 
luminescence in most absorbing systems, according to Section 95, 
are responsible for values of Q smaller than 100% in fluorescent 
systems. All quenching processes which depend on the varying dis- 
tances between excited and other molecules will obey the Stern- 
Volmer equation in their dependence on the number of "effective 
.collisions," regardless of the specific mechanism by which the ex- 
citation energy is consumed.* 

Processes such as spontaneous predissociation and internal con- 
version, which reduce the fluorescence yield regardless of external 
conditions, have been characterized as "internal quenching" or 
"quenching of the second kind" by some authors. These processes 
are constitutional features of the luminescent molecules themselves. 
In this book the term "quenching" is used only for processes by which 
the luminescence of a given compound is reduced below the intensity 
which the same compound would exhibit in the absence of the 
quenching agent (912). 

In order to measure the yield experimentally, two methods are in 
general use. In the first method the depth of the fluorescing layer or 
the concentration of a fluorescent solution is made so great that the 
exciting radiation is completely absorbed in it. If the fluorescence is 
observed backward (from the same side from which the primary light 
enters the solution), the brightness of the fluorescence is directly 
proportional to the efficiency under variable conditions (temperature, 
nature of the solvent, etc.) . This remains true, even if the concentration 
of the fluorescent molecules is changed, as long as Beer's law is valid, 
since in this case the absorption of the exciting radiation and the 
reabsorption of the fluorescence are determined only by the number 
of absorbing molecules in the paths of the two beams and this number 

* It has been known since the early Franck-Cario experiment on the 
mercury-sensitized photodissociation of H 8 that the primary quenching process 
is frequently a chemical reaction. This long-established fact is merely reasserted 
by the recently repeated derivation of the Stern- Volmer equation for the 
quenching of the fluorescence in liquid solutions by chemical reactions (1806). 



DEFINITION AND MEASUREMENT OF LUMINESCENCE YIELD 315 

is not altered by a change in concentration. For the second method, 
fluorescent layers of such reduced thickness or small concentration are 
used that the intensity of the exciting light along the path within the 
fluorescing medium can be supposed to be constant. In this case the 
absorption coefficient of the fluorescent substance for the exciting 
radiation must be determined separately in order to calculate Q, and 
corrections for the reabsorption of the fluorescence must also be 
introduced. 

While measurements of the relative efficiency Q r under variable 
conditions are comparatively simple, absolute values of Q are much 
more difficult to obtain and the corresponding data are scarce and 
not too reliable. For experiments of this kind the intensities of the 
exciting and of the secondary radiation must be measured in the same 
units and, therefore, the spectral sensitivity curve of the measuring 
instrument (photocell or photographic plate) must be known, or, in 
visual photometry, a spectrophotometer and a light source with 
known spectral intensity distribution must be used for comparison. 
Furthermore, the fluorescence intensity, which is measured directly 
only within a certain solid angle, has to be integrated over the whole 
sphere. The assumptions which have to be made for this purpose are 
not quite unequivocal, as will be discussed in Section 122. 

Vavilov, who was the first to measure the absolute yield Q for a 
dye solution, used the method of visual photometry; his results cannot 
claim an accuracy greater than 10 %. Within these limits they are 
in fairly good agreement with those obtained by Hellstroem who used 
a similar method for the determination of the fluorescence yield of 
various dye solutions. Among these was etioporphyrin dissolved in 
ether with the exceedingly low yield of 0.08%. Bowen determined Q 
for anthracene dissolved in benzene by means of his "heterochromatic 
photometer" (see Section 8). All other data concerning absolute fluo- 
rescence yields which are found in literature are derived from relative 
determinations and subsequent comparison with Vavilov's value for 
uranin or Bowen 's result for anthracene (Table 53) {i45>599< 1 74 8 )- 

106. Efficiency, Lifetime, and Solvent Quenching. The yields 
obtained for different compounds in the same solvent and for one 
compound in different solvents, which are illustrated in Table 53, are 
scattered over a very wide range. In his first paper on the fluorometric 
measurement of the lifetimes of fluorescent dye solutions, Gaviola 
pointed out that the solutions with the weakest fluorescence were 
those for which he found the smallest r-values, and he concluded that 
the probability of a radiating transition was of the same order for all 



316 



CONDENSED SYSTEMS 



Table 53 
Fluqrescknce Yield Q of Various Compounds in Different 





S 


OLVENl 


■S* AT 


Room Tem: 


=>ERATURE 








Compound 


Solvent 


Q in % 


T-10» 

(sec) 


Compound 


Solvent 


Cin% 


t (sec) 


Uranin . . 


Water 


71 


5 


Anthracene 


Paraffin 


23 








Ethanol 


71 


5 




Benzene 


25 









Glycerol 


71 


5 




Acetone 
Hexane 


21 

18f 


— 




Eosin . . 


Water 
Ethanol 


15 
40 


1.9 




Trichloro- 
methane 


17 


— 






Glycerol 


60 


— 


Naphtha- 


Cryst.=j= 
Xylene 


~100 
6 


— 




Erythrosin . . 


Water 
Water- 


2 


0.08 


cene 


Cry st. 
anthra- 




— 






acetone 


18 


— 




cene 


~100 


— 






Acetone 


50 


— 




Cryst.=}= 


2(?) 


— 




Rose bengale. 


Water 


1 


— 


Rubrene . . 


Benzene 


70 


— 






Acetone 


40 


— 




Acetone 

Cryst.=}= 


~100 

10(?) 







Rhodamine B 


Water 


25 


0.94 














Ethanol 


42 


1.6 


Uranyl . . 
sulfate 


Water 
H 2 S0 4 


1 

26 


10~ 4 

10- 2 




Potassium 


Water 


4.5 


2.5 




Cryst.=j= 


~100 


3-10- 2 




cyano- 










Canary 


20-100 


3-10-10" 


-4 


platinite . . 


Cry st. =}= 


~100 






glass § 









* All data listed in this table refer to measurements made in the presence of 
atmospheric air, so that the solvents -were not free of oxygen. 

t According to Samburski and Wolfsohn, the fluorescence yield of anthracene 
is larger by about 50% in hexane than in benzene. The discrepancy may due to 
the fact that the anthracene concentration was 25 times larger in Bowen's 
experiments and that self-quenching is much stronger in hexane than in benzene 
(compare Table 66) (145,140? b). 

=j= Cryst. : in the pure crystalline state. 

§ Varying with composition of canary glass. 

of these compounds and that short lifetimes and small efficiency were 
both due to quenching or another competing process {462a). 
The equation: 



t/t = I/I = Q 



(67) 



was derived in Section 3 from the Stern- Volmer formula; l/r = a 
is the probability of a radiating transition and /„ the fluorescence 
intensity corresponding to a yield of 100 %. This value of I cannot be 
found, in general, even in the absence of all intentional quenching, 



EFFICIENCY, LIFETIME, AND SOLVENT QUENCHING 317 

because of the existence of internal conversion. If the transition pro- 
bability a or the intensity of the absorption band remains unchanged, 
Equation (67) can be replaced by : 

Tx/r, = h/h = Qr ( 68 > 

where I 1: t v I 2 , t 2 , are the fluorescence intensities and lifetimes under 
two different conditions and Q r is the relative efficiency. 

Thus, Gaviola's qualitative conclusions were well founded 
theoretically, since the absorption coefficients of the dyes which he 
investigated were of the same order of magnitude while the fluo- 
rescence yields differed widely. With small transition probabilities and 
correspondingly weak absorption bands (e.g., for aqueous uranyl-salt 
solutions) however, a small fluorescence yield can be consistent with 
relatively long lifetimes. 

Whatever the nature of the competing mechanism which causes 
a low fluorescence yield, its chance of weakening or eventually 
completely destroying the luminescence will be the greater, the longer 
the natural lifetime t of the excited state. Thus, slow fluorescence and 
phosphorescence have a much greater probability of being quenched 
than normal fluorescence. On the other hand, long-lived luminescence 
processes can occur with an appreciable yield only if all competing 
processes are avoided. If a compound cannot be excited to fluorescence 
under any circumstances, although it is able to absorb light, the most 
probable interpretation is that it has a very high tendency to undergo 
internal conversion. Many dyes which are not fluorescent in liquid 
solutions become fluorescent and even phosphorescent when they have 
lost a part of their free mobility by being dissolved in a sQlid (sugar, 
boric acid, formic acid, etc.) or when they are absorbed on a rigid 
gel _ for instance, silica gel, alumina, or gelatin (the system dye- 
gelatin is frequently spoken of as a solid solution). Apparently the loss 
of certain degrees of freedom renders the process of internal conversion 
less probable. Examples of dyes of this type are discussed in Section 
137. Their formulas show distinctly that their structure is less rigid 
than that of other dyes of similar nature and similar absorption 
properties which are fluorescent in liquid solutions. Dyes of the latter 
type also become phosphorescent under the conditions which were 
described above (1454,1835). 

Although the ability of fluores€ing in a liquid solution is to some 
degree a property of the dissolved molecules as such, the fluorescence 
yield of a solution in which the excited molecules are in permanent 
contact with some other molecules depends greatly on the nature of 



318 CONDENSED SYSTEMS 

interaction with these molecules which may or may not quench the 
fluorescence. If the quenching probability is small, or, in other words, 
if some specific configuration in two colliding molecules (the excited 
and the quenching molecule) must be reached so that the excitation 
energy can be converted to heat or can initiate a chemical reaction, the 
fluorescence will not be quenched completely, even if a collision be- 
tween two complex molecules lasts a relatively long time and the ex- 
cited molecules are continuously in contact with one or the other of the 
quenching molecules. If one does not assume, however, that an excited 
molecule, once in contact with a quencher cannot react with a second 
quencher approaching from another direction, the quenching will still 
be increased by an increase in the quencher concentration, although 
it will no longer obey the Stern-Volmer equation. In the limiting case 
the excited molecules (and all other molecules of the fluorescent 
compound) are permanently and completely surrounded by "quenching 
molecules," namely, the molecules of the solvent. Nevertheless the 
probability of an energy transfer from excited molecules to solvent 
molecules is not large in comparison with the probability of fluo- 
rescence emission. Thus there is a continuous transition from the 
quenching by specific quenchers to the general case of "solvent 
quenching" which may be negligible in some cases and almost com- 
plete in others. 

Examples illustrating the different influence of solvent quenching 
of various solvents on similar fluorescent compounds are listed in 
Table 53. The number of such examples can be increased indefinitely. 
For instance, the fluorescence yield of benzopyrene is practically 
identical in solutions in petroleum ether, acetone, and pyridine; in the 
same solvents it varies for anthracene in the proportion of 4 : 5 : 9, 
and for 1 ,2-benzanthracene in the proportion 4 : 7 : 14 (io2g).* Still 
other examples are mentioned on the following pages. 

Substitution of halides for H-atoms in aromatic compounds 
reduces their fluorescence yield. The fluorescein series (fluorescein; 
eosin, erythrosin, and rose bengale) in Table 53 provides a characteris- 
tic example. However, a comparison of the fluorescence yields of 
fluorescein and erythrosin in water, on the one hand, and in acetone, 
on the other, proves the important part which the interaction between 
the fluorescent molecules and the solvent plays also in this instance. 

The figures listed in Table 53 refer to room temperature only. If 

* These figures were obtained with solutions completely free of oxygen and, 
therefore, are not distorted by the unequal solubility of oxygen in the various 
solvents; compare Section 108. 



EFFICIENCY, LIFETIME, AND SOLVENT QUENCHING 



319 



an alcoholic solution of uranin or rhodamine is cooled, Q increases 
at temperatures below 0° C by about 3 % per 10 degrees so that at 
— 80° C the yield is very nearly 100%, all internal conversion or 
quenching reactions having disappeared. In the case of erythrosin and 
rose bengale, which have an exceedingly low yield in alcohol at room 
temperature, the efficiency does not increase in the same way at low 
temperatures : the probability of internal conversion always remains 
large for these dyes, and this may be connected with their tendency 
to go over into a quasi-stable state (gi2) . 

The yield of the slow fluorescence of uranyl sulfate in sulfuric 
acid increases from 26% to almost 100% when the temperature is 
lowered from + 20° C to — 40° C, and the duration of the afterglow 
increases simultaneously by a corresponding amount. The fluorescence 
of an alcoholic solution of barium cyanoplatinite, which has an 
extremely short lifetime, becomes about four times stronger if the 
solution is cooled from room temperature to — 21° C. In all these 
instances the direct influence of low temperature was not separated 
from that of increasing viscosity. The fluorescence yield of anthracene 
dissolved in solid paraffin does not vary appreciably when the tempera- 
ture varies from the melting point to — 42° C {535, 77 5 J7 54)- 

On the other hand, the fluorescence yield practically always 
drops if a solution is heated above room temperature. (Concerning an 
important exception, compare Section 114). For uranyl sulfate in 
sulfuric acid the values of Q and r are shown for a considerable temper- 
ature range in Table 54. The existence of a similar parallelism between 
Q and r was proved for the same solution when the sulfuric acid was 
gradually diluted with water. Aqueous solutions of uranyl salts lose 



Table 54 

Yield and Duration of the Fluorescence of Uranyl Sulfate in 

Sulfuric Acid as a Function of Temperature 



Temp, in ° C . . . . 


18.5 


27 


45 


52 


67 


Q 


26 


21 


13 


11 


7.3 


T-10 4 


1.08 


0.81 


0.58 


0.46 


0.33 


Q/r-W 


24 


25 


22 


23 


22 



Table 55 
Fluorescence Yield of Rhodamine B in Glycerol as a Function 

of Temperature 



Temp, in ° C 
Q .. .. 



16 
75 



20 
70 



30 
64 



35 

60 



40 
55 



55 
44 



60 
40 



70 
32 



75 
28 



85 
25 



90 
21 



320 CONDENSED SYSTEMS 

their fluorescence power completely at temperatures which are always 
below the boiling point and, frequently, even much lower. The same 
is true for the solutions of the cyanoplatinites, in both cases with no 
important change in the absorbing power. 

Most dye solutions obey the same law. As an example, Table 55 
shows the relative fluorescence yield of rhodamine B in glycerol for 
the temperature range between 16° and 90° C, the absorption power 
again remaining constant. In other solvents, like isobutyl alcohol, the 
absorption spectrum of this dye varies greatly with increasing temper- 
ature, so that a loss of fluorescence yield might be ascribed to a change 
in the structure of the molecules. 

The fluorescence yield of quinoline red in aqueous or alcoholic 
solutions however is practically independent of temperature in the 
wide range from 0° to 100° C. Measurements of the corresponding 
lifetimes have not been performed (339,732). 

In principle, the heat of activation of the process causing the 
quenching can be derived, irrespective of the nature of the process, 
from the temperature dependence of the fluorescence yield. 

The decrease in the fluorescence yield of rubrene dissolved in 
aliphatic solvents from nearly 100% at' — 60° C to a much lower vulue 
at + 60° C has been ascribed to an increasing probability of internal 
conversion, and from the slope of the curves representing the log of the 
quenching constant (Eq. 7a) versus 1/7" the "heat of activation" 
corresponding to the height of point C above point A in Figure 84 
has been calculated to be about 7 kcal. This heat of activation is not 
a characteristic constant of the molecule itself, however, but is appa- 
rently determined by the fact that the rubrene molecules are sur- 
rounded by specific solvent molecules, for the fluorescence of rubrene 
dissolved in hexane shows an almost constant yield of nearly 100 % in 
the entire temperature range from — 60 to + 60° C ; thus, no internal 
conversion does occur in the rubrene molecules under these conditions. 

When dissolved in an aromatic solvent (benzene, toluene), ru- 
brene exhibits a fluorescence yield well below 100 % even at low 
temperatures. The fluorescence yield of anthracene at room tempera- 
ture is also lower by 35 % when the solvent is benzene than when it is 
hexane. This behavior has been .interpreted as due to the tendency of 
the aromatic solvent molecules to form complexes with the solute 
molecules, with the additional assumption that internal conversion 
has a relatively high probability in these complexes. With rising 
temperature the complexes dissociate and the resulting gain in fluo- 
rescence yield is claimed to compensate partially the increasing 



EFFICIENCY, LIFETIME, AND SOLVENT QUENCHING 321 

probability of internal conversion in the nonassociated rubrene mole- 
cules. Therefore, the fluorescence yield decreases less rapidly with 
rising temperature in aromatic solvents than in aliphatic solvents. 

It must be kept in mind, however, that increasing internal con- 
version is not the only possible interpretation of a temperature- 
dependent fluorescence yield. The decrease in yield can be explained 
also by some reversible photochemical reaction (such as the exchange 
of a hydrogen atom) between excited molecules and the molecules of 
the solvent. In order to explain the behavior of rubrene in the different 
solutions by such a mechanism one would only have to introduce the 
very simple and plausible assumption that the heat of activation of the 
photochemical reaction is so high, when the solvent is a paraffin, that 
the reaction practically does not occur at all in the temperature range 
under consideration ; it is of the orderof 7 kcal per mole for the aliphatic 
solvents and essentially smaller for the aromatic solvents, so that in 
the latter the reaction has an appreciable probability even at — 60° C 
(143C1407V). 

If the rate of the back reaction is not too high, the occurrence 
of the chemical reaction may become observable by a reversible 
bleaching such as has been obtained in solutions of chlorophyll. If, on 
the other hand, the back reaction follows the reaction within an 
extremely short interval, the process might be represented by the 
transient formation of a complex in which the electronic excitation 
energy is converted with very high probability to vibrational energy. 
This concept differs from the one discussed above in that the hypo- 
thetical complexes are not permanently present but exist only during 
the short period during which an excited rubrene molecule combines 
with a solvent molecule. 

The parallelism between Q and t (see Table 54) is destroyed if the 
processes of absorption and emission occur in different parts of a 
complex molecule. In the organic europium compounds mentioned 
in Section 97, the duration of the emission process is determined in the 
main by the transition probability in the electronic system of the 
rare-earth ion and is influenced very little by temperature. On the 
other hand, the fluorescence yield depends on the probability of the 
energy transfer from the organic radical in which the light absorption 
takes place to the europium ion. The yield decreases if this probability 
is smaller than the probability of converting the energy into heat, and 
the latter probability is a function of temperature. Thus, the intensity 
of the fluorescence of europium picrate dissolved in a mixture of 
ethanol, ether, and isopentane is over fifty times as strong at — 190° C 



322 CONDENSED SYSTEMS 

as at room temperature, although the decay constant changes by not 
more than 30 %. Furthermore, the probability of internal conversion 
of the absorbed energy depends to a great extent on the nature of the 
salt and of the solvent. At room temperature the fluorescence intensity 
of the salicylaldehyde in alcoholic solution is only about 13% of the 
intensity emitted by the benzoylacetonate, while at liquid-air tempera- 
ture they are practically equal. At room temperature the fluorescence 
of the salicylaldehyde in alcoholic solution is much less bright than 
when the same compound is dissolved in toluene ; at — 80° C the 
fluorescence of the two solutions shows the same brightness. At low 
temperatures the fluorescence yield of all europium salts is close to 
100% (at least 85%) (1816). 

The formation of complexes can favor the appearance of fluo- 
rescence in liquid solutions quite as well as it can favor the processes 
of internal conversion. Certain metallic ions (Pb++ and Zn + +) which 
are not fluorescent when dissolved in pure water form fluorescent 
complexes of the type (PbCl 4 ) — if an alkali halide of high concentra- 
tion is added to the solution. The relatively weak fluorescence of 
the hydrated Tl+-ion in aqueous solution is also enormously enhanced 
by the addition of halide ions, while the nature of the added cations 
is of slight importance {521 ,522 ,617 ,1304). 

107. Quenching of Luminescence by Foreign Molecules of Low 
Concentration. The earliest observations of the quenching effect of 
certain salts, especially halides, on the fluorescence of dye solutions 
are due to Herschel and Stokes {1585). While in solvent quenching the 
luminescent molecules are in permanent contact with molecules of low 
quenching efficiency, the concentration of the quenching molecules is 
now so low that a specific reaction must be assumed to take place 
between them and the excited molecules in the relatively short periods 
during which the distance between them is sufficiently small. The 
frequency of these events, which may be called collisions, is pro- 
portional to the concentration c of the quencher. As pointed out in 
Section 105, the quenching efficiency as a function of c must obey the 
Stern- Volmer equation in its most general form : 

/ = 7 /(l + *t ) (69) 

t is the lifetime of the excited state in the absence of the quencher and 
z is the number of "effective collisions" per second. 

A first qualitative proof of the validity of this statement can be 
seen in the fact that, under otherwise similar conditions, the efficiency 
of a given quencher like KI is, in general, the greater, the longer the 



QUENCHING OF LUMINESCENCE BY FOREIGN MOLECULES 



323 



natural lifetime t of the excited molecule (Table 56). The much 
longer-lasting weak phosphorescence of some dyes in liquid so- 
lutions disappears at quencher concentrations which have no visible 
influence on the fluorescence intensity of the solution.* On the other 
hand, the duration of the emission becomes shorter with increasing 
concentration of the quencher; this has been shown to be true in many 
instances. 

Table 56 
Quenching Efficiency of Potassium Iodide in Aqueous Solutions 

of Fluorescent Compounds 
(t: lifetime of excited state; c*: concentration of KI in mole per liter 





at which Q* = s 


Q ; k: "reaction rate") 




Compound 


Uranyl 
sulfate 


Quinine 
sulfate 


Uranin 


Eosin 


Anthra- 
cene f 


Naphtha- 
lene t 


t^ .. .. 

C *4 . . . . 


10-« 
10- 4 
10 4 


4-10- 8 
10-2 
100 


4-10- 9 

10-1 

10 


1.9- 10~ 9 

2.7-10-1 

3-7 


2.5- 10-' 
6-10-2 
17 


? 

0.5 
2 



t In ethanol. 

=j= The values of T, c* , and k depend to a certain degree on the concentration of 
the fluorescent compounds and differ, therefore, within certain limits, in the 
papers by various investigators. 



A quantitative verification of the equation is much more difficult. 
For a gas, all factors determining the number of effective collisions are 
known, with the exception only of the "effective cross section," and the 
Stern- Volmer formula can be used to calculate its value if the lifetime 
t is found by some other experiment. In a liquid solution a great 
number of variables are to be considered and several of them are 
interdependent. The most important among these parameters are the 
temperature T, the viscosity 7?, the ionic strength /x, and the dielectric 
constant D. Within the temperature range obtainable with most 
liquids the direct effect of a variation of T will be negligible in com- 
parison to its influence on 77 and p. Finally, the nature of the solvent 
is not only important because it determines 77, D, and p, but also 
because the value which Q and t have in the absence of the quencher 
depends on it. Thus, if one studies the influence of the viscosity by 
varying the solvent (diluting glycerol with water) the simultaneous 
change of t must be taken into account. 

* See also Section 109 concerning the quenching of the phosphorescence of 
dyes absorbed on silica gel. 



324 



CONDENSED SYSTEMS 



If all other parameters are kept constant, the number of effective 
collisions is proportional to the concentration c of the quencher: 

0, = 1/(1— he) (70) 

the value of t now being included in the constant k. k is the ' 'reaction 
rate" and is the reciprocal of the half-value concentration c* at which 
the yield Q* = §Q . Hence, the points in a diagram plotting l/Q r 
versus c should lie on a straight line which intersects the zero axis at 
the point l/Q r = 1. 

For values of \JQ r not exceeding 5, the experimental results 
agree fairly well with Equation (70) (Figure 108), while for greater 

concentrations of the quencher 
the deviations become much 
larger than the possible errors. 
Only within the same range of 
concentrations does Equation 
(68) hold for the relation be- 
tween Q r and t (434^755)- 

Vavilov tried to interpret 
these deviations by assuming 
a "configuration-quenching" to 
be superimposed on the col- 
lision-quenching. Those mole- 
cules in the "effective volume" of which a quenching molecule is 
present at the moment of absorption are assumed to lose their exci- 
tation energy by this configuration-quenching. In the absence of any 
collisions (with all molecules at rest in a very viscous medium) the 
relative yield is, therefore : 







^ 








^° 1 


1 


| «/« 



Fig. 108. Quenching of the fluorescence 
of fluorescein sodium in aqueous solu- 
tion by KI of various concentrations 

(Vavilov). 



Qr 



(71) 



where a> = tt\p 3 is the effective volume of the excited molecules and 
Nc the number of quenching molecules per cc.f By superposition of 
the two effects the relation between Q r and c becomes now : 



Qr= T 



+ he 



(72) 



Vavilov's own measurements of the quenching of the fluorescence of 
various dye solutions seem to be in good agreement with this last 
equation. 

The denominator in the fraction representing Q, does not contain 

•f c is the number of g/cc and N the number of molecules per g. 



QUENCHING OF LUMINESCENCE BY FOREIGN MOLECULES 325 

the parameter t and, thus, the linear relation between 1/t and c is 
preserved. Szymanowski, who determined t and Q r for several fluo- 
rescent solutions at various concentrations of KI as quenching agent, 
found 1/Q r to be represented as a function of c by a curve corresponding 
to Equation (72), while 1/t was represented within the same range of 
c by a straight line (Figure 109) (434,1600a). 

Rollefson and Stoughton have shown that a formula of the type 
of Equation (70) or (72) can be correct only if the fluorescent molecules 



i°l^ 




O 2 4 6 8-10" 

CONCENTRATION Of KI OCT 2 g/cc = 6 -lO^molar) 

Fig. 109. Yield and lifetime of fluorescence of fluores- 
cein sodium in water quenched by KI (Szymanowski). 
a: ljQ r . b: t /t. 



carry no electric charge or if the ionic strength is kept constant. 
According to these authors, the quenching process must be treated as 
a normal bimolecular reaction between the excited molecule and the 
quencher, regardless of the mechanism of the quenching reaction : 
D* + X ~* (DX) -> D + X + E 

where D is the fluorescent and X the quenching molecule, and E is 
the excitation energy which is set free and which may appear in any 
form. If D and X are ions, as is very frequently the case, the reaction 
rate k depends on the ionic strength of the solution, which is appreci- 
ably changed if the concentration of the quencher becomes large. On 
the other hand, the quenching efficiency of a given quencher at con- 
stant concentration varies a good deal if the ionic strength of the 
solution is changed by addition of an ionized salt which alone has no 
influence on the fluorescence yield of the solution. Table 56A show 
the change of k at constant KI concentration when the ionic strength 
Pringsheim 12 



326 



CONDENSED SYSTEMS 



of a fluorescein solution is varied by addition of sodium perchlorate. 
In the case of acridone which is electrically neutral, the addition of 
potassium nitrate is practically without influence on k. 

Table 56A 

Quenching Rate k of KI in Fluorescent Solution 

of Varying Ionic Strength y, 



Fluorescein + sodium perchlorate 



0.031 
11.4 



0.51 
12.2 



0.101 
14.0 



0.201 
16.4 



0.301 
16.8 



Acridone -f- potassium nitrate 



0.01 
92 



0.05 
92 



0.11 
94 



0.21 
93.5 



Similar effects should be brought about by variations of the dielectric 
constant, but no quantitative measurements are available (158?). 

Respecting the influence of the viscosity -q, Vavilov and others 
assumed that, since the velocity of diffusion decreases with increasing 
viscosity, k should be inversely proportional to 77. The following 
equation was derived by Vavilov for the relation between k and -q : 



k = 



r n RT (p + (T a ) (a 1 + a t ) 
3r] o t ■ <7 2 



(73) 



a! and o- 2 are the kinetic radii of the excited and the quenching mole- 
cules which, together with the viscosity, determine the velocity of 
diffusion; p is the effective radius of the excited molecules which 
depends on the nature of the solvent, even for the reaction between 
a specific fluorescent compound and a specific quencher. 

The figures in the first columns of Table 60 show that the efficiency 
of various quenchers is greater in methanol than in water, and greater 
in water than in ethanol, in the same order as the viscosities of these 
solvents vary. However, not even in this qualitative way is the rule 
valid in all instances. Thus, the quenching efficiency of potassium 
iodide for the fluorescence of fluorescein is greater in water (17 = 0.01 1) 
than in acetone (77 = 0.004). 

As a matter of fact, the fundamental assumption from which 
Equation (73) is derived is valid only in a very restricted sense. The 
number of collisions in a solution is not proportional to the velocity 
of diffusion and inversely proportional to the viscosity. In a viscous 
medium an individual quenching molecule has a reduced probability 
of hitting a second excited molecule after a collision with a first 
excited molecule, but ithasan increased probability of making a second 
collision or even a whole group of collisions with the first molecule 
within a short period of time (so-called cage effect) ; it may even happen 



QUENCHING OF LUMINESCENCE BY FOREIGN MOLECULES 327 

that such a group merges into a single collision of relatively long du- 
ration. Thus, the probability of quenching the fluorescence of this 
individual molecule is enhanced if the quenching efficiency of a single 
collision is less than 100%. The lower the quenching efficiency, the 
less it is affected by the viscosity of the solution. 

Moreover, the latter can be varied only by either mixing two 
liquids of widely different viscosities or by using solvents which differ 
in. viscosity and otherwise have similar properties, or by varying the 
temperature. The duration t of the fluorescence which would prevail 



- 




^7 


- 




r x 


s% 


/ 




/ / 






i s 

' 1 




i 



0.4 0.8 

O 



i-'o- 2 



- 








- 




k* • 




. 




s 




"/* .■ 










1 


i 





0.4 0.8 

b 



'** 



Fig. 110. Quenching of the fluorescence of fluorescein (a) by potas- 
sium iodide and (b) by aniline as a function of viscosity [Sveshnikov 

(1600)] 
(«) (6) 

O sugar solution • isobutyl alcohol 

# mixtures of glycerol with O ethyl alcohol 

water & mixture of isobutyl alcohol 

with ethyl alcohol 
A mixture of glycerol with iso- 
butyl alcohol 
+ glycerol 

in the absence of the quencher can be altered by such variations and 
this must influence the value of k in Equation (73), irrespective of 
simultaneous changes in viscosity. The formation of solvate envelopes 
protecting the fluorescent molecules against the action of a quencher 
will also depend on the nature of the solvent. 

Sveshnikov discussed these various influences which, in general, 
are difficult to separate.* However, plotting \jQ versus l/ v a.ndT/r), 
respectively, for a variety of solutions and quenchers, he obtained a 
series of curves which closely resembled those reproduced in Figures 

* These problems have been treated recently in a more quantitative 
manner by LaMer and co-workers (625a, 1723a, 1843). 



328 



CONDENSED SYSTEMS 



1 10a and b. In the experiments, rj was varied by changing the con- 
centration of aqueous sugar solutions, by adding water to glycerol, 
by using a series of alcohols, and by altering their temperature; 
potassium iodide, the organic compounds listed in Table 60, and 
copper sulfate served as quenchers, and the fluorescent compounds 
were sodium naphthionate, rhodamine B, fluorescein, and rhoduline 
red. All points belonging to a given pair of fluorescent compound and 
quencher were situated on smooth curves of similar shape. They prove 
the existence of general parallelism between \JQ and l/i? and of sys- 
tematic deviations from the linear relation between the two para- 
meters, especially at high viscosities (1600a). 

108. Specific Properties of Quenchers. Quenching substances can 
be divided into several classes with widely differing quenching efficien- 
cies for different groups of fluorescent solutions. In the first systematic 
research of this kind Jette, West, and Muller found that if potassium 
salts were added t6 aqueous solutions of uranin, quinine sulfate, and 
uranyl sulfate, the quenching efficiency of various anions for every one 
of these three solutions followed the order {689,1091,1823) : 

I-, CNS-, Br-, C1-, C a 4 -- C 2 H 3 2 - SO". NO s ~ F~. 

The efficiency of the ions to the right of Cl~ is very small. These re- 
sults were confirmed for solutions of eosin, rhodamine, and other 
dyes. It has been pointed out that the order of the quenching efficien- 
cies is the same as the order of the deformabilities of the ions. It is 
also the order of many other of their properties, however, and a direct 
relation between the quenching capacity and the deformability of an 
ion is not obvious. Besides, the relative efficiency of two quenchers, 
even when they are as closely related as I~ and Br, depends a great 

Table 57 
Relative Quenching Efficiency (Half- Value Concentration c*) 

OF THE HALIDE IONS IN AQUEOUS SOLUTIONS 

(c* = 1 for I - as quencher) 





Color of fluorescence 


Quenching ion 


Fluorescing compound 


I- 


Br- 


ci- 






c* 


Quinine sulfate . . . . 


blue 
green-yellow 

blue 
green-yellow 


1 
1 
1 
1 


1.4 
20 
20 

1 


3.9 
100 




100 


Pinacryptol yellow 


1.5 



SPECIFIC PROPERTIES OF QUENCHERS 



329 



deal on the nature of the fluorescent compound. The examples listed 
in Table 57 show that there is no general connection between the 
sensitivity of a quencher and the color of fluorescence, which is a 
measure of the energy stored in the fluorescent molecules. 

Rollefson and Stoughton have shown that for another group of 
fluorescent compounds the order of quenching efficiencies is exactly 
reversed, so that N0 3 - and BrO s - are much stronger quenchers than 
I- Sodium naphthionate, a-naphthol, and sodium sulfanilate belong 
to this group (1588). 

Table 58 
Quenching Efficiency (Half-Value Con- 
centration c* and "Reaction Rate" k) of 
Various Negative Ions for Sodium 
Naphthionate 



Quencher. . . . 


N0 S - 


BiO a - 


I- 


c* 

k 


0.061 
16.4 


0.057 
17.5 


2.4 
0.42 



The colorless cations K+,Na+ Ca 4 -+, Ba++, etc., have no quenching 
effect and can be interchanged in the salts used as quenchers without 
appreciable influence on the fluorescence yield. Small effects are 
produced in some cases by the ions of rare-earth metals such as Sm +++ 
and Pr+++, while the colored ions Cu++, Ni++, and Fe++ act as strong 
quenchers in most fluorescent solutions. The values collected in Table 59 
were calculated taking into account the fraction of the incident light 
which is absorbed by the quenching ions. The very high efficiency of 

Table 58 

Quenching of Fluorescence by Positive Ions 

(Half -Value Concentration c* and k) 



Fluorescent 
compound 


Quinine sulfate 


Esculin 


Sodium 
naphthionate 


Thallous 
chloride 


Solvent 


HjSO.-HjO 


Ethanol 


Water 


H 2 O-KCl(10-») 




c* 


* 


c* 


k 


c* 


k 


c» 


k 


Quencher : 
CuS0 4 . . 
NiS0 4 . . 
(VO)S0 4 
FeS0 4 .. 
CoS0 4 . . 
Cr,(S0 4 ), 
MnS0 4 . 


0.275 

0.189 

0.099 

0.036 

0.021 

0.0063 

2.05 


3.6 
5.3 

10.1 

28 

48 
158 
0.49 


0.028 

0.100 

0.070 

0.136 

0.016 

0.0062 

1.16 


35.7 

10 

14.3 

7.3 
62.5 
159 

0.86 


0.007 
0.050 

0.010 
0.005 


143 
20 

100 
200 


lO"" 3 


1000 



330 



CONDENSED SYSTEMS 



the chromium ions and the relatively small effect produced by man- 
ganese is noteworthy (1792). 

The fluorescence of the complex ions which are formed when 
thallous salts are dissolved in pure water and in solutions of KCI and 
KBr is also quenched by Fe++ and by I+; the effect is strongest in 
the chloride solutions, a good deal weaker in pure water, and weakest 
for the complexes formed in bromide solutions, while the fluorescence 
yield (and probably the lifetime of the excited state) is about equal for 
the halogen complexes and much smaller for the Tl+-ions in pure 
water (1521,1522). 

Many organic compounds are powerful quenchers for practically 
all fluorescent solutions. A few examples are given in Table 60. The 
strong fluorescence of uranyl sulfate in sulfuric acid is almost com- 
pletely suppressed by the presence of traces of ethanol, while the 
fluorescence yield of dyes dissolved in ethanol is relatively high in 
most cases (272,346). 



Table 60 

The Quenching of Fluorescent Solutions by Organic Compounds 

(Molar half -value concentration c*) 



Fluorescent 

compound 


Quinine 


sulfate 


Pinacryptol yellow 


Sodium 

naphthion- 

ate 


Esculin 




Methanol 


Water 


Water 


Ethanol 


Water 


Ethanol 




0.006 


0.011 


0.011 


0.012 


0.011 


0.010 




c* 


Quencher : 
Phenol . . 
o-Cresol . . 
Hydroquinone . 
Resorcinol 

Pyrogallol 
a-Naphthol 


0.010 

0.0046 
0.0067 
0.0063 


0.013 
0.012 
0.010 
0.011 
0.011 
0.100 


0.071 

0.39 

0.042 

0.031 

0.049 

0.037 


0.098 
0.070 
0.076 
0.068 
0.052 
0.050 
0.042 


0.60 

1.0 

0.041 

2.90 

0.20 

0.082 


0.40 

2.03 

0.13 

0.505 

0.188 

0.108 

0.081 



An exceptional behavior is shown by an alcoholic solution of 
rhodamine B to which increasing quantities of nitrobenzene are added. 
In the right-hand part of Figure 1 1 le, the initial rise of !/(?, is of the 
usual type, but, after reaching a maximum at a nitrobenzene content 
of 4 moles per liter of solution, the curve slopes downward again, so 
that the fluorescence yield in pure nitrobenzene is restored to nearly 
one-half of its value in pure ethanol. The fluorescence and absorption 
spectra of rhodamine are practically identical in both solutions. The 



SPECIFIC PROPERTIES OF QUENCHERS 



331 



parallelism between thcurves fe or \JQ r and 1/t indicates a quenching 
obeying the Stern -Volmer law (1600a). 

If only the left-hand or only the right-hand branch of the curves 
were known, one would assume that one of the two liquids is a solvent 





/ » 
r 

•fA--^" -4 


c 

V-~^ jt Ijll — * 


1; ' 

C-B b-&- gl a 



0.1 



0.2 O 

c in mole/liter 



0.1 



0.2 




20 40 60 80 

NITROBENZENE CONCENTRATION 



100% 



Fig. 111. Specific quenching power of various sub- 
stances (Sveshnikov) : (a) rhodamine B, (b) anthra- 
cene, (c) sodium naphthionate, (d) quinine sulfate, 
(e) rhodamine B in ethanol-nitrobenzene mixture. 

3: aniline; #: KI; A : hydroquinone ; 
^: guaiacol; O: nitrobenzene. 



in which the fluorescence yield is fairly good, while the other is a 
strong quencher. The complete curves suggest, however, that while 
neither of the two solvents strongly quenches the fluorescence, in 
mixtures of alcohol and nitrobenzene some sort of complexes are 
formed with a peak equilibrium concentration in a mixture of 70 % 
alcohol and 40 % nitrobenzene, and that the excited rhodamine mole- 



332 CONDENSED SYSTEMS 

cules are quenched by collisions with these complexes rather than by 
interaction with the molecules of the individual solvents themselves. 

Quenching curves which were obtained by Banderet appear, at 
first sight, to be very similar to the curve of Figure llle, but corre- 
spond probably to an essentially different mechanism. The quenchers 
were organic compounds consisting of long chains such as gardinol 
[CH 3 -(CH 2 ) 15 -S0 3 ]-Na+ sodium stearate [CH 3 -(CH 2 ) 15 -COO]-Na+ and 
sapamine [CHa^CH^^CH^CH^CH^^CO-NHg-fCH^^N^H^^+Cl- 
which were added to aqueous solutions of rhodamine, pyronine, 
and quinine sulfate or of fluorescein, eosin, and iris blue. With increas- 
ing concentration of the quencher the fluorescence of the solutions 
was almost completely suppressed, but when the concentration of 
the quencher exceeded 10 volume per cent, the intensity of the fluo- 
rescence increased again and reached about 60 to 70 % of its initial 
value, when the concentration of the quencher attained 50 volume 
per cent. Simultaneously, the solution was converted into a gel and 
this is apparently the reason for the vanishing quenching effect. The 
recovery of the fluorescence yield is best observed at very low dye 
concentrations, but occurs also at higher concentrations of the fluo- 
rescing molecules. A second very striking peculiarity is characteristic 
of these quenchers. Only positive fluorescent ions (rhodamine, quinine 
sulfate) are strongly quenched by the compounds which form nega- 
tive ions (gardenal, sodium stearate), while negative fluorescent ions 
(fluorescein, eosin) are quenched by the compounds which form posi- 
tive ions (saponin and similar substances) (49). In these cases quench- 
ing becomes effective only when the dye molecules are adsorbed on 
the long chains of the quenching compounds. 

The quenching of fluorescence by molecular oxygen is of special 
interest for more than one reason. It is to be kept in mind that the 
2 -concentration in atmospheric air is less than 0.01 mole per liter, 
and that it is very low in all liquid solutions, even if they are saturated 
with oxygen under an oxygen pressure of 760 mm (Table 61). There- 
fore, even relatively small decreases in fluorescence yield of oxygen- 
saturated solutions correspond to rather high values of ^(Cy. These 

Table 61 
Oxygen Concentration c in Liquids under 760 mm 2 (mole/liter)* 



Liquid 


Hexane Acetone 


Toluene 


Benzene 


Alcohol 


Water 


c-10 3 


15 1 9 


7.5 


7.15 


6.3 


1.3 



* These are not the units found in most tables. 



SPECIFIC PROPERTIES OF QUENCHERS 333 

values are, again, widely different for different fluorescent compounds. 
For the fluorescence of uranin, eosin, erythrosin and rhodamine G 
extra in water k(0 2 ) is practically zero [1476). However, the phos- 
phorescence of eosin, erythrosin, phloxin, and other dyes in liquid 
solutions is completely quenched by small traces of 2 {136,745). 
According to Kautsky, the fluorescence of trypaflavine is quenched 
only slightly by oxygen when the dye is dissolved in water; it is 
quenched a little more in alcoholic and still more in ace tonic solutions. 
This order corresponds to the increasing solubility of oxygen in these 
solvents. The fluorescence of chlorophyll dissolved in alcohol or 
acetone is from 20 to 40 per cent weaker when the solutions are 
saturated with oxygen in atmospheric air than in the absence of 2 ; 
the corresponding values of k(0 2 ) are 250 and 700, respectively. 

Under continuous illumination most dye solutions are slowly 
bleached, if all oxygen is not carefully removed. The photo-oxidation 
may be due mainly to the reaction of molecules in quasi-stable states, 
as will be explained in the next section. 

An earlier hypothesis, which at present is interesting merely from 
the historical point of view, supposed that every fluorescence process 
was only a secondary phenomenon accompanying a permanent 
photochemical conversion of the luminescent molecule (1202-1206, 
1210,1211,1279,1281). However, it could be shown that such con- 
versions, as a rule, occur only in the presence of oxygen or another 
quencher, and that the fluorescence is strongest when the solution 
does not undergo any chemical reaction (1799). In many cases a direct 
photochemical transformation of a fluorescent compound is brought 
about by light of shorter wavelengths. Thus, esculin loses its fluo- 
rescence power under the action of near-ultraviolet radiation in so- 
lutions containing oxygen, while in a solution free of oxygen a loss of 
fluorescence is observed only after irradiation with light of wavelengths 
below 3000A (999). The same is true for certain aromatic compounds 
dissolved in solid boric acid (1691) . 

Oxygen quenches the fluorescence of many aromatic hydro- 
carbons in liquid solutions. The third column of Table 61 A lists the 
quenching constant k of oxygen for hydrocarbons dissolved in hexane ; 
the values of k are spread out over a wide range without showing any 
systematic order. A comparison between naphthalene and anthracene 
is striking: naphthalene, which is almost immune to I~-ions, is ex- 
ceedingly sensitive to the quenching by oxygen; the fluorescence of 
anthracene, much less sensitive to oxygen, is very appreciably 
quenched by iodine ions. No relation can be established between the 



334 



CONDENSED SYSTEMS 



Table 61A 

Fluorescence Yield Q and Quenching Constant k of Aromatic 
Hydrocarbons Dissolved in Hexane and Excited 

by THE Hg-LlNE 2537A 



Compound 


<?in% 


k 


Compound 


Q in % 


A 


Toluene 

^"-Xylene 

Trimethylbenzene . 
Tetramethylbenzene 


10.9 

22.7 

28.7 

30 

41.5 

16.4 

52.3 


600 
1100 
1060 

800 
1050 

850 

980 


Naphthalene 
Anthracene . . . 
Phenanthrene 




37.6 
46,3 
27 
100 
70.4 
22.8 
23.2 


2400 
178 
960 
530 


Acenaphthene 


2200 
440 


Triphenylmethane 


580 



quenching efficiency of oxygen and the number of fused rings of which 
a compound consists; the sensitivity of benzanthracene and benzo- 
pyrene is intermediate between those of anthracene and naphthalene 
{144-146). 

Nitric oxide quenches the fluorescence of aromatic hydrocarbons 
with about the same efficiency as oxygen. In both instances the 
quenching is completely reversible. When the quenching oxygen or 
nitric oxide is flushed out by some inert gas, such as nitrogen or 
hydrogen, the solution recovers its full fluorescence intensity {1805, 
1806). 

The phosphorescence of dyes absorbed on silica gel is observed 
only in a very high vacuum or in an atmosphere in which the partial 
pressure of oxygen does not exceed 10~ 3 mm.* The phosphorescence 
is weakened appreciably even by oxygen at 10~ 5 mm; in the case of 
trypaflavine, the intensity drops to one-half at a partial oxygen 
pressure of 5- 10 -5 mm (426,748). 

The fluorescence of the adsorbed dye is also quenched to a certain 
extent by oxygen, but since the lifetime of the excited state is less 
than 10~ 8 sec (compared to nearly 1 sec for the phosphorescence), 
much higher oxygen pressures are needed for producing an appreciable 
effect. The fluorescence of trypaflavine adsorbed on silica gel is almost 
half as large in atmospheric air as in a high vacuum. The fluorescence 



* Nitric oxide and certain vapors may also act as quenchers for this 
phosphorescence. Kautsky's observation, according to which the trypaflavine 
phosphorescence is quenched by water vapor, however, has been proved to be 
caused by a secondary effect. Traces of oxygen which are absorbed on the gel 
are dislodged by the vapor and then quench the phosphorescence. If they are 
removed, the vapor itself has no influence on the afterglow (426). 



MECHANISM OF QUENCHING BY FOREIGN MOLECULES 335 

of eosin, erythrosin, and rhodamine B is as little affected by the 
presence of oxygen when the dyes are adsorbed on either aluminum 
oxide or silica gel,* as they are in aqueous solutions; on the other 
hand, the fluorescence of chlorophyll is considerably more sensitive 
to the action of oxygen than the trypaflavine fluorescence, also under 
these conditions (426,749). 

The blue fluorescence of organic compounds that can be prepared 
in the form of aero-gels, such as palmitic acid and the solid polymers 
of formaldehyde, is very strongly and reversibly quenched by the 
vapors of nitrobenzene and quinone; the vapors of dimethylaniline 
and diacetyl are appreciably less efficient, and the vapors of mono- 
bromoethane, benzene, and ammonia, and all permanent gases, in- 
cluding oxygen, produce practically n'o quenching in this instance 
(1640b). 

109. Mechanism of Quenching by Foreign Molecules. If addition 
of foreign molecules to a fluorescent solution converts the fluorescent 
molecules by a dark reaction into molecules of another kind which are 
non fluorescent, the foreign molecules do not "quench" the fluorescence 
in the sense in which the term is employed here. If the newly formed 
molecules do not absorb the exciting light, the fluorescence intensity 
will be altered because of the decrease in concentration of fluorescent 
molecules, but the fluorescence yield will remain unchanged. If, on the 
other hand, the newly formed molecules absorb a part of the exciting 
light, an apparent decrease in fluorescence yield will result exactly as 
if some other kind of inactive light-absorbing molecules had been 
introduced into the solution. However, this apparent loss of yield 
would not be accompanied by the corresponding decrease in t which 
is the distinctive characteristic of genuine quenching (as it was in the 
case of fluorescent vapors) and which follows from the laws expressed 
by the Stern- Volmer equation. 

The overall result of a genuine quenching reaction can consist in 
the chemical transformation of the excited molecule, of the quencher, 
or of a third kind of molecule — for instance, of the solvent. If no 
permanent change is produced in the solution by the quenching 
process, the excitation energy must eventually have been converted 
into heat. These overall effects, however, do not provide much knowl- 
edge concerning the elementary quenching processes. 

If the phosphorescence of trypaflavine adsorbed on silica gel is 

* The negative ions of the fluorescein derivatives are adsorbed on alumina, 
but not on silica, while the opposite is true for the positive ions of basic dyes, 
e.g., trypaflavine and rhodamine. 



336 CONDENSED SYSTEMS 

quenched by oxygen at low pressure, the oxygen will disappear after 
a period of continuous irradiation and the dye will be discolored and 
no longer luminescent ; it will be oxidized. This oxidation is probably 
not the primary quenching process, as Kautsky seems to have proved 
by a very clever experiment : if a colorless and nonfluorescent leuco 
dye, e.g., leucomalachite green, is absorbed together with trypaflavine 
on the gel, the trypaflavine phosphorescence is quenched by oxygen 
as before, but it is the leuco dye which is oxidized to malachite green 
with its characteristic blue-green color. This oxidation does not occur 
under conditions which are identical, except that no trypaflavine is 
present. Thus, the primary quenching process must consist in the 
formation of some highly reactive gas which is able in a subsequent 
collision to oxidize a trypaflavine or leucomalachite-green molecule, 
the second reaction having by far the greater probability (740,745, 
749). Kautsky assumed that the intermediate product was a metastable 
oxygen molecule, but this hypothesis must be discarded for many 
reasons (455,456,742,743,746). According to Franck, the primary 
reaction is represented by the equation : DH* + 2 -> D + H0 2 , DH 
being the dye in its normal state and the radical H0 2 the oxidizing 
agent. 

The relatively weak photo-oxidation by which many dyes are 
discolored in liquid solutions saturated with oxygen is reduced by 
the addition of other foreign molecules which are able to quench the 
fluorescence of the dye. According to J. and F. Perrin, the negative 
halide ions and organic compounds such as hydroquinone, phenol, 
and aniline are examples of "antioxidants" of this type. Their effi- 
ciency in inhibiting the oxidation is much greater than their efficiency 
in quenching the fluorescence of the dyes. Quantitative measurements 
comparing the two effects are available only for a solution of eosin in 
glycerol (136). They seem to prove that the antioxidant efficiency is 
equal to the efficiency in quenching the phosphorescence of the dye 
solution and it may be concluded from this experiment that molecules 
in the quasi-stable state contribute most to the photo-oxidation 
process (1219,1777). 

The chemical reaction which is directly correlated to the 
quenching process may be so speedily reversible that it is not ob- 
served under normal circumstances. The fluorescence of a large class 
of dye solutions is quenched by iodide ions. For thionine ("Lauth's 
Violet"), J. Weiss was able to observe an appreciable, though weak, 
bleaching effect under strong illumination when the fluorescence of 
the dye solution was partially inhibited by an addition of potassium 



MECHANISM OF QUENCHING BY FOREIGN MOLECULES 337 

iodide. This discoloration is due to the conversion of the dye into 
its leuco base: 




NH, 



Immediately after the end of the irradiation, the normal absorbing 
power of the solution was restored spontaneously. A similar, but still 
weaker, effect was obtained with an eosin solution, and it is not im- 
probable that reversible conversions of the same kind with an even 
higher rate of reversibility occur in many other dye solutions. 

However, even in these apparently simple cases the conversion 
into the leuco dye was not supposed to be the primary quenching 
process; the latter, according to Weiss, is characterized by the re- 
action : D* + I - -*■ D~ + I. The subsequent chemical reactions are 
beyond the scope of this discussion. In the same way, Weiss explains 
the quenching of a fluorescent solution by ferrous ions: D* + Fe ++ -> 
D~ + Fe+++. His hypothesis that the electron transfer which is 
supposed to be the primary cause of the quenching should be due to 
a "resonance" is not acceptable on any theoretical grounds. The 
mechanism itself may be effective in some cases but is by no means as 
general as Weiss asserts (1809-1812). 

F. Pen-in assumed that the energy of excitation of a fluorescent 
molecule is spent in separating the extra electron from a halogen ion 
in a collision of the second kind; the efficiency of a quencher was 
supposed to depend to a certain extent on the nature of the solvent 
because the energy of the electron affinity is a function of the dielectric 
constant of the surrounding medium. The energy, of the order of 
magnitude of 2.5 eV, which is stored in an excited molecule with 
visible fluorescence is, however, never sufficient for separating an 
I _ -ion from its electron, and, therefore, Franck and Livingston re- 
placed this process by' a reaction in which additional energy is supplied 
by the formation of a semiquinone DH, which, according to Weiss' 
hypothesis, would occur only in a secondary reaction of D~ and H 2 ; 
the quenching particle is not the isolated ion I - , but the complex ion 
I~OH 2 . The primary reaction: D* + I-OH 2 ^DH + I + OH~ is 
followed, in general, by a recombination : DH + I + OH - -> D + 
I~OH 2 . DH reacts with 2 to give D + H0 2 only if oxygen is present 



338 CONDENSED SYSTEMS 

in the solution at a sufficient concentration, and molecular iodine is 
formed, as was proved experimentally (423,424,12^,1221,1463). 

The quenching efficiency of oxygen in solutions of aromatic 
hydrocarbons is ascribed to the formation of peroxides of the type 



o 

1 
o 



The existence of peroxides of this type has been proved by Moureau 
and Duffraisse. Weil-Malherbe and Weiss obtained small quantities 
of analogous compounds in which 2 was replaced by NO ("nitrox- 
ides") by intensive irradiation of solutions of anthracene and djmethyl- 
benzanthracene in an atmosphere of nitric oxide (1805,1806). 

Only in some instances (benzene, toluene, the xylenes, and other 
methylbenzenes) is the decrease in fluorescence yield caused by the 
action of oxygen compensated by a corresponding yield of peroxides. 
For other hydrocarbons the rate of photo-oxidation is much smaller 
than the quenching of fluorescence would indicate ; the production of 
peroxides is below the limit of experimental error for naphthalene, a 
compound with a very large quenching constant k(0^), and for 
fluorene, which has a relatively small value of k(0^). Thus, no general 
simple relation between the quenching efficiency of 2 and the rate of 
photo-oxidation exists (143a, 146). In certain cases the complex formed 
by the collision of the excited hydrocarbon and the oxygen molecule 
must dissociate immediately after the quenching process has occurred. 
Hence, it is reasonable to assume that quenching processes are very 
frequently not connected with a chemical reaction in the ordinary 
sense of the word, but involve the formation of unstable intermediates 
which are able to convert the elctronic energy by internal conversion 
into thermal energy according to the equation*: D* + X -> (DX)* 
+ D+X+E kin . 

110. Fluorescent Compounds as Photosensitizers. The probabi- 
lity of a connection between the fluorescence of certain dyes like 
eosin or erythrosin and their usefulness in the sensitization of photo- 
graphic emulsions was pointed out by J. Stark long ago. All quenching 
processes mentioned in the last section in which, ultimately, some 
molecules other than those of the absorbing dye undergo a chemical 

* Compare the analogous considerations concerning the quenching of 
the fluorescence of vapors (Section 42) and the quenching by solvents (Section 
X06). 



FLUORESCENT COMPOUNDS AS PHOTOSENSITIZERS 339 

reaction might be quoted as further examples in favor of this hy- 
pothesis. It need hardly be repeated that it is not the fluorescence it- 
self but the quenching of the fluorescence which is essential for the 
transfer of energy to the -reacting molecule. The parallelism between 
the two phenomena is caused by the ability of the compounds to store 
the excitation energy which they have acquired by light absorption, 
for a relatively long period without dissipating it into heat. The best 
sensitizers, however, are not the dyes with the highest fluorescence 
yield, such as fluorescein, but rather those which show comparatively 
weak fluorescence and are able to phosphoresce even in liquid so- 
lution. (Compare Section 131). Their great inclination to pass into a 
quasi-stable state would cause their small fluorescence yield as well 
as their greater propensity to act as sensitizers. The dyes which, at 
present, are used as the best sensitizers for photographic emulsions, 
the various cyanine dyes, are not fluorescent at all in liquid solutions. 
Some of these dyes are brightly fluorescent, however, when they are 
dissolved in aqueous gelatin, and they retain a part of this fluores- 
cence even when they are adsorbed as sensitizers to the silver salt 
in a photographic emulsion. If the emulsion is supersensitized by 
addition of another dye not absorbing in the same spectral region 
[for instance, l-(^-diethylaminostyryl)benzothiazole], the fluores- 
cence of the cyanine dye is completely quenched and its sensitizing 
efficiency is enormously enhanced ; under these conditions the whole 
excitation energy is made available for the sensitizing process. Ad- 
dition of the "super-sensitizing" dye to the silver-free cyanine solution 
in gelatin quenches also the much stronger fluorescence of this solu- 
tion with exceedingly high efficiency (1822a). It seems that the primary 
process in the interaction between the molecules of the supersensitizing 
dye and the excited molecules of the sensitizing dye consists of an 
internal conversion by which the excitation energy is transformed into 
vibrational energy of the whole complex and thus becomes available 
for the ejection of an electron from a Br~-ion in the silver bromide 
emulsion. (For the very interesting fluorescence of cyanine dyes in a 
state of high polymerization compare Section 115.) 

The acceleration of the photolysis of ethyl iodide in alcoholic 
solution by the addition of naphthalene may be discussed as a typical 
example of a photochemical reaction which can be sensitized in a 
liquid solution by a fluorescent compound. C 2 H 5 I has a diffuse ab- 
sorption band between 2300 and 3200A ; absorption of the Hg-lines at 
3 1 30A decomposes the molecules into an ethyl radical and a free I-atom 
with a quantum yield of 30%. The fluorescence of naphthalene in 



340 



CONDENSED SYSTEMS 




alcoholic solution is strongly quenched by ethyl iodide, k q being 180. 
If the fluorescence is almost completely quenched by an iodide con- 
centration above 0.01 molar, the increase of the rate of decomposition 
of the iodide is directly proportional to the absorption caused by the 
sensitizer. If the absorption of the mercury line is trebled by the 
addition of an adequate quantity of naphthalene to the solution, the 

rate of photolysis also becomes three 
times as large as in the solution free of 
naphthalene. The photochemical yield 
remains unaltered at 30%; this means 
tl \ \. that the total energy which is absorbed 

' n N. \ by the naphthalene molecules, including 

the fraction which does not appear as 
fluorescence under any conditions be- 
cause of internal conversion, is trans- 
ferred to the ethyl iodine molecules. The 
relatively low photochemical yield is 
ascribed to the probability of initial 
recombination of the radical and the 
iodine atom (1822b). 

The energy which is needed for 
the transition from the lower vibra- 
tional levels to the repulsion curve may be much larger than the 
dissociation energy, as shown in Figure 112. In a collision between 
an excited naphthalene molecule D* and an ethyl iodide molecule Et, 
either the shape of the normal repulsion curve can be altered to A' so 
that the distance from the nonvibrating state of Et to the repulsion 
curve is reduced to a value not exceeding the energy stored in D*, 
or by a process of internal conversion occurring in the "complex" 
(DEt) * this energy is converted directly into high vibrational energy 
of the ground state N of Et which suffices to dissociate the latter. In 
either case the ethyl iodide molecules in the low vibrational states 
corresponding to thermal equilibrium can take part in the process 
(which, therefore, acquires a high degree of probability). (The same 
consideration applies to all sensitized photochemical reactions and 
especially to those which cannot be produced directly by light of the 
wavelength which is active in the sensitized process.) 

In a solvent of great viscosity the quenching power of ethyl iodide 
for the naphthalene fluorescence and the photosensitizing power of 
naphthalene for the photolysis of ethyl iodide become smaller. 

The fluorescence of jS-naphthol is very little quenched by ethyl 



Fig. 112. Potential curves 
for the photosensitized de- 
composition of ethyl iodide. 



FLUORESCENT COMPOUNDS AS PHOTOSENSITIZERS 341 

iodide (k q — 14) and /J-naphthol has a very small sensitizing effect on 
the photolysis of ethyl iodide. On the other hand, the naphthalene 
fluorescence is only very slightly quenched by potassium iodide 
(k q = 2), which makes it certain that the quenching is not caused by 
I _ -ions. Finally, the total light absorption in a solution containing 
naphthalene and ethyl iodide is the sum of the absorption by each 
of the two compounds and, therefore, it is not to be assumed that the 
two compounds form a complex which would be responsible for the 
increase in the rate of decomposition. In this case all observations 
agree with the assumption that the sensitization is caused by collisions 
of the second kind. 

Not every sensitization of a photochemical process by a lumi- 
nescent compound, however, can be treated as an energy transfer in 
a collision process. The sensitized photolysis of oxalic acid in aqueous 
solution in the presence of uranyl sulfate is a typical example of a 
process of this kind. The fluorescence of the uranyl salt is weakened by 
the addition of oxalic acid and simultaneously the acid is decomposed 
by the action of the light which is absorbed by the uranyl salt. KI, 
with a much higher quenching efficiency, also inhibits the photolysis 
of the acid if both are present in the solution. However, the photo- 
chemical process is reduced to about one-fourth of its maximum value 
by a 0.1 molar KI concentration, while the uranyl fluorescence is 
almost completely quenched by a KI concentration which is about a 
hundred times smaller. Hence, the energy transfer from excited uranyl 
molecules to the acid molecules is practically uninhibited by a con- 
centration of I~-ions sufficient to deactivate every excited uranyl 
radical during its relatively long lifetime. Apparently, uranyl-oxalic 
acid complexes are formed independently of the irradiation, and light 
absorbed by the uranyl radicals in these complexes is transferred to 
the other part of the complex within a time which is short compared to 
the lifetime of the isolated excited uranyl ions. Thus, it can also be 
understood why the yield of the photochemical reaction is of the order 
of magnitude 60 %, while the fluorescence yield in the aqueous uranyl 
salt solution scarcely exceeds 1 %. The existence of complexes in this 
case is made even more probable by a very marked influence of the 
addition of oxalic acid on the absorption spectrum ; although the latter 
retains the structure characteristic of all uranyl salt spectra, the ab- 
sorbing power in the near-ultraviolet region is more than doubled by 
addition of an equimolecular- quantity of oxalic acid, while oxalic 
acid itself shows no absorption at all in this spectral region (212, 
1288,1808). 



342 CONDENSED SYSTEMS 

There are other instances of the sensitization of photochemical 
processes by fluorescing compounds which are ascribed to the for- 
mation of complexes. Schpolsky and Sheremetiev mention the oxida- 
tion of sodium sulfite in an aqueous solution of rhodamine, and Eder's 
reaction, 2HgCl 2 + (NH 4 ) 2 C 2 4 -> Hg 2 Cl 2 + 2NH 4 C1 + 2C0 2 , in the 
presence of eosin under irradiation with light absorbed by the dyes 
as belonging to this class. If a dye is absorbed on some foreign mole- 
cules in a solid solution, it is especially difficult to draw a sharp limit ; 
some authors are of the opinion that in photographic emulsions which 
are sensitized with dyes of the fluorescein series, the silver atoms and 
the dyes form complexes such as silver erythrosinates and that a 
reaction of this type is greatly favored if the acidity of the dye is 
increased by the substitution of halogens for hydrogen atoms {1476). 

Very little is known concerning the existence of sensitized fluo- 
rescence in liquid solutions. In general, the absorption bands are so 
broad that it is difficult to prove that the fluorescence of an additional 
dye is not excited by light absorption in the "tail" of its own ab- 
sorption band rather than by energy transfer from another dye the 
absorption peak of which has a wavelength coinciding with that of the 
primary radiation, while its fluorescence band corresponds to the 
absorption band of the "sensitized" dye. The excitation of the red 
fluorescence of fluorescent blue in an aqueous solution of pheno- 
safranine is the only example quoted in the literature ; the fluorescence 
of the latter dye is yellow and is excited, together with the red fluo- 
rescence of the former, by absorption of green light. A case of sensitized 
dye fluorescence in which the primary energy is provided by a chemical 
reaction instead of irradiation has been described by Kautsky and 
Zocher. If siloxene is oxidized by potassium permanganate, it emits 
a weak bluish chemiluminescence. If dyes such as rhodamine and 
eosin are absorbed on the gel, the characteristic fluorescence of the dye 
is emitted with great intensity as long as the process of oxidation 
lasts {755,1214). 

Quenching of the fluorescence of one dye by the addition of an- 
other dye to the solution has been observed more frequently. According 
to Perrin, the efficiency is greater the more closely the absorption band 
of the second dye coincides with the fluorescence band of the first dye, 
and he therefore ascribes the energy transfer to a "resonance in- 
duction" without giving a very clear idea of the mechanism by which 
the excitation energy is converted into heat. However, a reabsorption 
of the fluorescence light would produce the same effect, and it is 
difficult to distinguish between these two causes of decreasing fluo- 



FLUORESCENCE OF LIVING PLANTS 343 

rescence intensity. Examples quoted by Perrin are the quenching of 
the fluorescence of uranin and of fluorescent blue by eosin and by 
methylene blue, respectively (i20j,i2og,i2i2). 

A phenomenon which might be called sensitized fluorescence 
occurs with naphthacene and some other colored hydrocarbons 
dissolved in small concentrations in crystalline anthracene, when the 
fluorescence of the dissolved compound is excited by light which is 
absorbed by the molecules of the solid solvent. These cases will be 
treated in Section 1 1 7. 

As a last type of reaction which can be sensitized by fluorescent 
dyes, the coagulation of colloids such as arsenic sulfate may be 
mentioned. If such a solution is irradiated in the presence of an 
electrolyte (e.g., lithium chloride) and a dye (e.g., eosin), the rate of 
coagulation is highly increased. The sensitization is inhibited by 
addition of an "antioxidant" which, under other circumstances, 
would quench the fluorescence of the dye (132) . 

111. Fluorescence of Living Plants. Photosynthesis, the assimi- 
lation of carbon dioxide by green plants under the action of light, 
is by far the most important of all photochemical reactions which are 
sensitized by a fluorescent dye. Chlorophyll, which exhibits fluo- 
rescence when it is dissolved in organic liquid solvents, is also fluo- 
rescent when adsorbed on the proteins of a plant leaf. The very 
characteristic luminescence spectrum is nearly the same in both cases ; 
however, the yield, which in alcoholic solutions is of the order of ten 
per cent, is far below one per cent in plants. This small fluorescence 
yield is not exclusively due to the energy transfer in sensitizing photo- 
synthesis, but is caused to a considerable degree by other competing 
"inactive" quenching processes according to the generalized Stern- 
Volmer equation : 

Q'=7Tf+l (74) 

where Q f is the fluorescence yield and a, /?, y aTe the relative proba- 
bilities of fluorescence, inactive quenching, and sensitization. 

Photosynthesis is a highly complicated process with the overall 
reaction : 

n {CO a + H 2 + xhv} -+ (CH a O) M + n0 2 + Energy (75) 

The reaction takes place in a series of successive steps in which several 
catalysts cooperate. Several [probably x = 8 in Equation (75)] of 
these steps require an activation energy which is provided by light 



344 



CONDENSED SYSTEMS 



0/T 

A 



absorption in the chlorophyll molecules.* Under normal conditions, 
about one-third of the absorbed light energy is lost by inactive 
quenching. The chemical reactions themselves are not within the 
scope of this discussion, which is concerned only with the fluorescence 
phenomena associated with photosynthesis (41 5, 7 r ja, 7 '44, 7 50, 7 ^1, 753). 

Once more the fluorescing 
molecules are those which have 
no part in the sensitizing action : 
fluorescence yield and rate of 
photosynthesis are antiparallel, 
although because of the contri- 
bution of inactive quenching, 
they are not strictly comple- 
mentary. If photosynthesis is 
slowed down by external con- 
ditions — for instance, by low 
temperature or small C0 2 -con- 
centration in the surrounding 
atmosphere — the fluorescence 
output is enhanced; every in- 
crease of the photosynthesis rate 
is accompanied by decreasing 
fluorescence. The maximum out- 
put of at least one stage of the 
photochemical process is limited by the limited supply of the catalyst 
which is needed for the reaction. If a leaf is subjected to a steady irra- 
diation and if the light input is not too large, fluorescence intensity 
and the rate of the photochemical reaction are proportional to the 
intensity of the impinging light : fluorescence yield and the yield of 
photosynthesis are independent of the intensity of the exciting light 
under these conditions. With increasing light intensity, however, 
photosynthesis tends toward a saturation value corresponding to the 
total quantity of catalyst available for one of the reaction stages. 
Simultaneously, the fluorescence yield increases and approaches a 
value which is about 70% higher than the yield obtained at low 
light intensities. From there on the fluorescence intensity is again 

* A part of the energy which is supplied in successive steps by the transfer 
of a photon is not used up for the reactions and, therefore, appears on the right 
side of the overall equation as "Energy." This has nothing to do with the 
"inactive quenching processes" which are characterized by the probability 
coefficient f} in Equation (74) . 



140 



120 



100 



20 



40 80 120 160 

LIGHT INTENSITY X I0 3 erg/cm* we 

Fig. 113. Yield of fluorescence and 
photosynthesis in a leaf as a func- 
tion of the intensity of illumination 
(Franck, French, and Puck) . 

a: relative fluorescence yield. 
b: relative yield of photosyn- 
thesis, c: rate of photosyn- 
thesis. 



FLUORESCENCE OF LI-VING PLANTS 



345 



proportional to the intensity of the exciting light, the yield now 
remaining constant at the higher level (Figure 113). Not all of the 
energy which is withheld from the photochemical process is gained 
for the fluorescence process, but if one of the principal paths hy which 
excitation energy can be lost is blocked by the saturation of the 
catalyst, the number of excited molecules in equilibrium with ab- 
sorbed radiation becomes larger and the fluorescence intensity, there- 
fore, increases. 

Inhibition of photosynthesis by a poison, such as hydrogen 
cyanide, or by low temperature, causes the rise of fluorescence yield 
to occur at much lower light intensities. Under very weak and very 
strong illumination, the fluorescence of inhibited and uninhibited 
leaves is the same. In the first case, the very low rate of the photo- 
chemical reaction is carried on even in an inhibited leaf, while, in the 
second case, the fraction of the absorbed radiation needed for the 
saturation of photosynthesis in the uninhibited leaf is practically 
negligible. 

Much additional understanding of the whole problem is gained by 
the observation of leaves during the so-called induction period. If a 
leaf which has been kept in the dark for some time is irradiated, the 
fluorescence starts at the same intensity level which is characteristic 
of the state of equilibrium under continuous irradiation. Its intensity 
increases rapidly during the first second until it reaches a value which 
is about three times as large as the initial value. The absolute magni- 
tude of this fluorescence outburst depends on the intensity of the 
exciting light. It is proportional to the primary intensity if the latter 
is not too high, but above a certain critical limit a further increase in 
exciting light intensity produces only a small increase in the fluo- 
rescence outburst. The rate of this initial rise of fluorescence also 
increases with the light intensity and approaches an upper limit which 







C) 


/ 






/ 

1 


1 


1 









- 




U>) 


^ 






. 






— 

1 







20 



100 









(f) 




K 










h 


~o~ | 


-°i 


c 


— i 



40 80 120 160 sec 



Fig. 114. Fluorescence intensity of ,a leaf as a function of the time of 

illumination (Franck, French, and Puck) : (a) during the Jirst 3 sec. ; 

(b) during the first 50 sec; and (c) during the first 3 min. 



346 CONDENSED SYSTEMS 

it can not exceed. The temperature and the C0 2 -concentration of the 
surrounding atmosphere do not influence the rate or the intensity of 
the outburst (Figure 114) {415,431,740,749,751,753). 

When the fluorescence has reached its maximum intensity at 
the end of the outburst, it decays again, under normal conditions 
during several minutes, until it has dropped to the initial level. From 
there on it remains steady for a practically indefinite time. The decay 
from the peak of the outburst is inhibited by high concentration of 
carbon dioxide ; it is slowed down by low temperature, by poisoning 
the leaf with hydrogen cyanide, and by a shortage of oxygen in the 
surrounding atmosphere. Every one of these treatments impedes not 
only photosynthesis but also the respiration process. Evidently the 
decay of fluorescence is due to the second of these effects, since it also 
occurs when the leaf is kept in the dark after the end of the fluo- 
rescence outburst. If the illumination is interrupted for a short time 
at the peak of the outburst, fluorescence starts at a higher level 
when the irradiation is renewed; it takes a dark period of about 10 sec 
before the normal "dark state" of the leaf is restored. 

The whole courseof the fluorescence intensity during the induction 
period under various conditions is represented in a plausible manner 
by Franck and Herzf eld's theory of photosynthesis, which cannot be 
discussed here at length {420). As far as the fluorescence phenomena 
are concerned, the theory explains how the coefficient y of Equation 
(74) decreases at first during the induction period and, after having 
reached a minimum, increases again, until an equilibrium state is 
attained. 

The quantitative measurements of the fluorescence intensity 
during the induction period show that the "inactive quenching" is 
also influenced by the distribution of the intermediate products of 
photosynthesis, or that the probability coefficient j8 in Equation (74) 
is not constant. The fluorescence peak at the end of the "outburst" is 
almost twice as high as the fluorescence intensity observed during the 
steady state, when photosynthesis is inhibited. Apparently the mole- 
cules in direct contact with the chlorophyll molecules are not the 
same in both cases and the probability of a quenching energy transfer 
is altered. This inconstancy of /S renders the relation between fluo- 
rescence yield and photosynthesis rate more complicated and increases 
the difficulty of finding any quantitative correlation between the two 
processes. 

112. The "Optimum Concentration". In many publications the 
concentrations of fluorescent compounds are given in g per cc of the 



THE OPTIMUM CONCENTRATION 



347 



solvent, while other authors refer their measurements to molar con- 
centrations. The following Table 62 may be useful for the conversion 
of the various data from one system to the other. The figures are of the 
same order of magnitude in either system and this may lead to misun- 
derstandings. 

Table 62 

Conversion of the Concentrations of Fluorescent Compounds 
from Gram per Cubic Centimeter to Mole per Liter 

(10- 3 g/cc = #-10- 3 mole/liter; 10~ 3 mole/liter = y-10~ 3 g/cc) 



Compound 



Molecular 
weight M 



Fluorescein 

Eosin 

Erythrosin 

Rose bengale 

Rhodamine B extra . . 

Rhodamine 6G 

Trypaflavine 

Euthrysine 

Rhoduline orange . . 

Magdala red 

Thionine 

y-Isocyanine 

Malachite green 

Crystal violet 

Quinine sulfate (+ 7H 2 0) 



370 
692 
879.4 
1017.2 
446.5 
450.5 
259.5 
301.5 
401.5 
486.5 
263.5 
362 
346.5 
390.5 
492 



2.7 

1.44 

1.14 

0.98 

2.24 

2.22 

3.85 

3.31 

2.95 

2.06 

3.79 

2.76 

2.88 

2.54 

2.07 



0.37 

0.69 

0.88 

1.02 

0.446 

0.45 

0.26 

0.30 

0.40 

0.49 

0.26 

0.36 

0.35 

0.39 

0.49 



The fluorescence strength F in a solution is determined by the 
number of photons emitted by a unit volume when light of unity 
intensity enters the volume through one of its surfaces. If Beer's law 
is assumed to be valid, it follows that : 



F = {l—e-°)Q 



(76a) 



e being the molar absorption coefficient, c the concentration in moles 
per liter, and Q the quantum yield. For small values of c the equation 
can be replaced by : 



&Q 



(76b) 



As long as this is permissible, the fluorescence strength increases 
proportionally to the concentration. The exact proportionality be- 
tween F and c was proved, for instance, by quantitative measurements 



348 



CONDENSED SYSTEMS 



performed with aqueous rhodamine solutions in a range of concen- 
trations between 10 -9 and 10~* g per cc. Uranin can be traced by its 
fluorescence at concentrations as low as 10 -14 g per cc at which there 
are only a few thousand molecules in a cubic millimeter. In such dilute 
solutions, the fluorescence strength can be used directly for quanti- 
tative analysis. 

On the other hand, Equation (76a) tends toward the limit : 



F=Q 



(76c) 



when the value of c becomes very large ; the fluorescence strength is 
equal to the yield at concentrations at which practically all incident 











■A 


~"^-^/ 


\ \ 










\ 


/ 






\ 



-5 -4 

LOG (Tl + ) 



-3 




Fig. 115. Yield and apparent 
fluorescence intensity / (1), 
and relative fluorescence 
Q r (2) of Tl + in a concen- 
trated KC1 solution as a 
function of the Tl-concen- 
tration (Pringsheim and 
Vogels) . 



mole/liter 



Fig. 116. Yield, (Q r ), lifetime 
(t/t ), and polarization (p/po) 
of the fluorescence of fluorescein 
sodium in glycerol as a function 
of the dye concentration 
( Vavilov) . 



light is absorbed in the volume under observation. F should asymp- 
totically approach this limiting value, and simultaneously the light- 
emitting volume should contract itself with increasing brightness into 
a thin surface layer. This is almost never the behavior which is actually 
observed in a fluorescent solution, when the concentration of the 
fluorescent molecules is increased gradually. After having reached a 
maximum, F decreases again, and frequently the solution does not. 
fluorescence at all at very high concentrations (Figures J 15-1 18) 
Such a behavior can be due only to the fact that Q itself is not constant, 
but is a function of c. It cannot be explained by the assumption that at 



SELF-QUENCHING 



349 



12 



h"l^ 



3 |o8 



1° f 

r A 



4 

CONCENTRATION 



8 12 

c IN I0" 3 g/cc 

,-3 „ 



high concentrations a part of the fluorescent light is reabsorbed in the 
solution if the luminescence is observed backward or from the side 
from which the exciting light enters (compare Section 105). 

The existence of an "optimum concentration" is a very general 
phenomenon in fluorescent solutions. It even occurs quite regularly in 
solutions of substances which, like the uranyl salts and anthracene, 
are strongly luminescent in the pure solid state. Compounds as widely 
different as most dyes in water, in 
alcohol or in sugar; uranyl sulfate 
in H 2 S0 4 or in water; benzene in 
alcohol or in hexane; and Tl+-ions 
in aqueous KC1 solutions, may be 
mentioned as examples of "self- 
quenching" (Figure 115). Pekerman 
states, however, that alcoholic so- 
lutions of numerous aromatic 
hydrocarbons and their derivatives, 
such as anthracene, naphthionic 
acid, quinine, esculin, etc. are free 
of self-quenching in a very wide 
range of concentrations (1200b). If an 
afterglow is observable in a so- 
lution, it is even more sensitive to 
this effect. Thus, the phosphores- 
cence of eosin in glycerol attains 
its greatest strength at a concen- 
tration of 5- 10~ 5 g per cc, while the 
fluorescence strength increases up to a concentration of 10 -3 g per cc. 
Similarly, the afterglow of hematoporphyrin in alcohol can be ob- 
served only at the very highest dilution. For uranin in solid boric 
acid, the fluorescence intensity and the initial brightness of the 
afterglow decrease at the same rate with increasing concentration 
of the dye. The duration of the afterglow decreases as well, however, 
and thus the total phosphorescence output is more strongly quenched 
than the fluorescence (178,750,911,1201b). 

113. Self-quenching. Two widely different theories have been put 
forward for the explanation of self -quenching.* Both are supported 
by some experimental evidence, but neither is sufficient to explain 
all observed facts and it is probable that each contains a part of 

* A third hypothesis which, at its best, can be applied only to a very 
few specific cases will be mentioned in Section 116. 



(IO~ a g/cc = 3.2- I0" 3 mole/liter) 

Fig. 117. Yield and lifetime of 

the fluorescence of fluorescein 

sodium in water (a) and in 

glycerol (b) as a funct on of the 

dye concentration 

(Szymanowski). 

1 : yield. 2 : lifetime. 



350 



CONDENSED SYSTEMS 



truth. Vavilov and F. Perrin were the first to apply the hypothesis of 
collisions of the second kind to these quenching processes, assuming 
that because of some resonance phenomenon the effective cross- 
sections were particularly large for interactions between molecules of 
the same kind (1215,1216,1221,1224,1749,1758,1762a). A specific me- 
chanism by which this resonance should produce quenching has never 
been proposed. The other theory has been asserted by Walter at a very 
early date; more recently, Levshin and Rabinowitch have been its 
principal champions (911,13170). According to these authors, the 



0-8 



r 



- 


' a 


^ 


/ 








■ 

1 


sec 

1 



0.4 



2 4 6-10' 

r 

Fig. 118. Fluorescence yield Q r as a function of the 
lifetime t of fluorescein and rhodamine fluorescence 
at various dye concentrations (Szymanowski). 
• fluorescein in water ; c from 0.175 to 6.8- 10- 3 g/cc 

O fluorescein in ethanol; c from 2.1 to 23-10-? 
■ fluorescein in isobutanol; c from 0.37 to 10.9- 10~ s 
A fluorescein in glycerol; c from 0.11 to 12- 10~ 3 
A rhodamine in methanol; c from 1.0 to 21.5- 10~ 3 



decrease in fluorescence yield with increasing concentration of the 
fluorescent compound is due to the formation of dimers or polymers 
which are not fluorescent. Such an effect would not be equivalent to 
genuine quenching, however, as was pointed out in the first paragraph 
of Section 109, and the apparent decrease in fluorescence yield would 
not be accompanied by a decrease in the lifetime t of those excited 
molecules which are not polymerized and which are the only molecules 
contributing to the fluorescence. 

The strongest argument in favor of the collision theory of self- 
quenching is the existence of the parallelism between the decrease in 
Q r and t with the increase in concentration of the fluorescent mole- 
cules. This parallelism appeared very clearly in a set of curves that 
were published by Gaviola and Pringsheim, who used Gaviola's 
first measurements of the lifetimes of the fluorescein fluorescence. 



SELF-QUENCHING 



351 



Szymanowski's later, more accurate measurements enabled Vavilov 
to replot these curves with slightly greater precision (Figure 116) 
(461, L). 

The self-quenching of uranyl sulfate in concentrated sulfuric acid 
follows the Stern- Volmer Equation (11) up to the highest concen- 
trations of the fluorescent molecule and Q r and t are proportional in 
the same range of concentrations. The problem is complicated by the 
increasing viscosity of the concentrated solutions, which has to be 
taken into account. The self-quenching of anthracene in benzene 
excited by near u.v. also obeys the Stern- Volmer law, but no t- 
values are available for these solutions (i2gi,ij54). 

While l/Q r and 1/t plotted versus c are well represented by 
straight lines for rhodamine B extra dissolved in methanol, the 
deviations from the Stern-Volmer law greatly exceed the possible 
errors for the same dye dissolved in glycerol, for uranin dissolved in 
water, ethanol, and isobutanol, and for many other dye solutions 
(Figure 1 17). An obvious discrepancy between the curves for Q r and r 
appears also in Figure 1 16. Nevertheless, Figure 1 18, in which the Q r - 
values of Table 63 are represented as a function of the corresponding 
r-values proves that, to the first approximation at least, a linear 
relation prevails between these two variables, and this is even more 
striking because the dye concentration are spread over a very wide 
range (1624). 

Table 63 

Lifetimes (in lCT 9 Sec) and Relative Quantum Yield Q r of the 
Fluorescence of Fluorescein as a Function of the Dye Con- 
centration C ( IN MG PER CC) IN VARIOUS SOLVENTS 



Water 


Ethanol 


Isobutanol 


Glycerol 


C 


T 


Qr 


C 


T 


Qr 


C 


T 


Qr 


C 


T 


Qr 


0.175 


5.07 


1.00 


2.1 


5.07 


1.00 


0.37 


5.07 


0.98 


0.12 


5.13 


0.'98 


0.66 


5.07 


0.96 


7.0 


3.87 


0.67 


4.5 


3.87 


0.67 


0.36 


5.13 


1.00 


1.57 


4.60 


0.69 


11.0 


2.13 


0.45 


6.0 


3.33 


0.5.7 


4.60 


3.67 


0.66 


2.00 


3.87 


0.57 


16.6 


1.20 


0.21 


7.4 


1.65 


0.45 


6.9 


3.2 


0.52 


2.82 


3.26 


0.39 


23 


0.67 


0.11 


9.0 


2.13 


0.31 


9.0 


2.67 


0.40 


4.6 


1.73 


0.18 


— 


— 


— 


10.9 


1.87 


0.21 


12.4 


2.1 


0.26 



Since, in many instances, the experimental values did not fit the 
collision theory of self-quenching, F. Perrin replaced it by a hypo- 
thesis which considered only the influence of the average configu- 



352 CONDENSED SYSTEMS 

ration of the molecules and not their relative motion. This hypothesis 
led to the equation : 

= Qo<>- kc ( 77a ) 

k is a constant depending mainly on a function f(r) which determines 
the quenching probability of an excited molecule by an unexcited 
molecule of the same kind at the mutual distance r {1215,1224). In 
order to explain the existence of an "optimum concentration," 
Bruninghaus and, later, Ewles have put forward a similar formula for 
the fluorescence strength: F = Ace~ nc ; however, a theoretical foun- 
dation for introduction of the exponential which causes the decrease 
in F after passing the optimum is not mentioned by either of the 
authors. Ewles postulates that a dye molecule is luminescent only 
when it is separated from the next dye molecule by some smallest 
number n of solvent molecules (178,181,371). Bouchard states that 
numerous measurements which he performed under varying experi- 
mental conditions with various dye solutions are in good agreement 
with Perrin's equation (133-135). Other investigators do not confirm 
this statement. 

As I pointed out incidentally, introduction of a quenching pro- 
bability determined by the function f(r) instead of the rigid "effective 
volume" of Eq. 71, restores the interdependence of Q andr, although, 
in general, the relation would not be linear; at any rate the molecules 
remaining longest in the excited state would have the greatest pro- 
bability of being quenched (329,330)- This principle is the basis of 
Vavilov's latest theory of self-quenching, which represents the self- 
quenching of dye solutions in the concentration range from 10 - * to 
10 _1 mole per liter, but fails to interpret the behavior at lower con- 
centrations which all previous theories also were unable to explain : in 
the curves plotting the yield and lifetime as functions of the con- 
centration, the decrease in Q and t sets in with a sharp bend at a 
certain "limiting concentration" c , while at lower concentrations the 
curves are nearly horizontal. This behavior has been observed in many 
instances, the value of c varying with the nature of the dye and of the 
solvent (Table 64). The polarization of the fluorescence, which will be 
discussed in Sections 118 and 119, decreases also with increasing 
concentration and is even more sensitive in this respect than Q and t 
(Figure 116) (1201b). 

Vavilov assumes the existence of two independent probabilities of 
energy transfer by resonance from an excited molecule to another 
molecule of the same kind, the one leading only to depolarization, the 



POLYMERIZATION AND SELF-QUENCHING 



353 



Table 64 
Limiting Molar Concentration c 
Which Self-quenching Begins 





Uranin 


Eosin 


Rhodamine 
6G 


Trypa- 
flavine 


Coriphos- 
phine 


Solvent : 












Water . . 


5-10- 4 


5-KT 4 


5-10- 6 


3.10- 3 


3.1 IT 4 


Ethanol . 


3-10- 3 


— 


l-icr 3 





— 


Acetone . 


— 


— 


1.4- lO" 3 


— 


— 


Glycerol . 


t-KT 3 


— 


1.10- 3 





— 



other to quenching, the first being much larger than the second. In 
addition to these time-dependent interactions, a static sphere of in- 
fluence is assumed for the quenching, in the same way as in Equations 
(71) and (72). From these assumptions the following equation is 
derived : 



Q=e-^\l + c(l + l + le-^)\ 



(77b) 



t is the lifetime of the excited molecules at lowest concentrations, 
Q the sphere of static influence, and 1 \k x and 1 jk^ determine the proba- 
bilities of quenching and depolarizing energy transfers. The equation 
represents with great accuracy the observed dependence of Q, t, 
and p on the concentration of four dyes dissolved in glycerol. It must 
be emphasized, however, that the theory is purely formalistic in that 
it fails also to interpret the mechanism by which the energy is con- 
verted into heat in the "quenching" transfers (1762a). 

114. Polymerization and Self-quenching. The absorption spectra 
of many dyes in solutions undergo a continuous change with increasing 
concentration, and this change is connected with the self-quenching of 
fluorescence by an unmistakable parallelism. Both effects depend in 
the same way on the nature of the dye and the solvent. For certain 
dyes the deviations from Beer's law in the normal absorption band 
(M) of the dissolved molecules are appreciable even at very low 
concentrations, especially in aqueous solutions (for instance, for 
rhodamine at 5- 10 -5 moles per liter and for thionine at 2- 10 -7 moles 
per liter); at higher concentrations new bands appear in the ab- 
sorption spectra and eventually these prevail almost alone. In alco- 
holic solutions the new bands ("D-bands") are observed only at 
greater dye concentrations and they may be completely missing in 



354 



CONDENSED SYSTEMS 



acetonic solutions in which no self-quenching occurs (Figure 1 19) (ojj, 

1523)- 

The D-bands are ascribed to dimers of the dye molecules. From 

the relative areas under the 
curves representing the ab- 
sorption bands the relative 
concentrations of monom- 
ers and dimers in the so- 
lution can be calculated. 
The results obtained by 
Rabinowitch and Epstein 
with aqueous solutions of 
thionine and methylene 
blue (Figure 120) were in 
good agreement with the 
equation for a partially 
dissociated molecule: 



600 



400 



200 




4600 5000 5400 5800 A 



Fig. 119. Absorption bands of eosin in 
aqueous solutions at various dye concen- 
trations (Soederberg). 
a: 2.5-10- 1 g/cc. 6:2-10- 2 . c: 3-10- 6 . 



k = 2c* a /(l — x) 



(78) 



where c is the total concentration of the dye and x the fraction of 
monomeric molecules or "dissociated polymers" (1317a). 

If a thionine solution is irradiated with light of a wavelength which 
is equally absorbed in. the two overlapping bands M and D, the fluo- 
rescence yield decreases at very nearly the same rate as the concen- 



4 - 



1 1 

ABSORPTION SPECTRUM 
OF THIONINE 


Y 
P 


*\ 




p» 3.5 in Woter 














no. concentrotion 


/r * 


* 1 




1 25 » I0" 3 2.03 


* — " 






2 25 x 10"* 4.08 






3 25 x I0" 8 529 /4 




A 




4 25 x IO-» 5.43 rfp 


\^. 1 


v\ 




5 2 


5 x lO" 7 5 


76 //ff 




\\ 






1 


+* t 

I 


r 1 t >* 





4000 



4500 



5000 



5500 
X(A) 



6000 



6500 



7000 



Fig. 120. Molar extinction coefficient of thionine in water 
[Rabinowitch and Epstein (jjj7«)] 



POLYMERIZATION AND SELF-QUENCHING 



355 



tration of monomeric molecules x. In ethanol, thionine does not 
polymerize and Q remains constant. 

Table 65 
Self-quenching and Dimerization of Thionine 
in Different Solvents 



Concentration 


In water 


In e 


hanol 


X 


Q, 


Q r l* 


X 


Qr 


2.5- io~ B 


0.995 


10 


10.5 


1.0 


20 


2.5- 10- 4 


0.732 


6.8 


9.3 


1.0 


19 


2.5- 10-' 


0.359 


2.7 


7.5 


1.0 


20 



0.8 


( . 
















Or 
0.4 


V 








V' 










1 


1 


==*= 







T* ■ 





8 16 24 

Concentration in g/cc 



32-10 



If, on the other hand, the fluorescence of an aqueous rhodamine 
solution which is excited by light of wavelength 5461A is compared 
with the fluorescence ex- 
cited by light of wavelength 
6000A, the decrease in yield 
with increasing concen- 
tration is much smaller in 
the first than in the second 
case : 6000Aand 5461 A cor- 
respond very nearly to the 
peaks of the D and the M- 
bandof the solution (Figure 
121) (or 3 ). 

If a solution is heated, 
the .D-band in the ab- 
sorption spectrum becomes 
weaker and the fluorescence 
yield simultaneously be- 
comes larger, while all losses of excitation energy due to internal con- 
version or to collision processes are increased by the increase in 
temperature. Only when a certain critical temperature is exceeded 
does the fluorescence yield begin to drop again, because the dimi- 
nishing polymerization is overcompensated by other quenching 
processes (Figure 122). 

Notwithstanding so much evidence, polymerization alone cannot 
be made responsible for self-quenching, as was pointed out in the last 
section. In some instances, as for thionine in water, polymerization 
may be the main cause, only the relatively small deviations shown in 
Table 65 being due to genuine quenching. In other instances, where the 



.-♦ 



Fig. 121. Self -quenching of the fluorescence 
of rhodamine in aqueous solution with in- 
creasing concentration (Levshin). 

a: exciting light of wavelength 5460A. 
b: exciting light of wavelength 5900A. 



356 



CONDENSED SYSTEMS 



2.0 



1.0 



0.5 



- -2 jcr 


c-43 -I0" 3 


1 


e = 25-IO -4 

I 



parallelism of Q and t has been proved to exist, some sort of collision- 
quenching must prevail and only the deviations from the theoretical 
equations can be caused by polymerization. It has been suggested that 
the polymerized molecules, apart from not being fluorescent them- 
selves, might have a large specific quenching efficiency for the non- 
associated molecules ; no reason is known why this should be any more 
probable than a strong quenching of the excited molecules by non- 
excited monomeric molecules. 

As a matter of fact, the latter possibility and the polymerization 

process might well be related. If, 
in a given solvent, polymerized 
molecules exist in a certain equili- 
brium concentration, this concen- 
tration can be shifted towards higher 
values if the solution is irradiated, 
or, in other words: dye molecules 
which are excited by light absorption 
are quenched by forming a dimer 
in a collision with a nonexcited 
molecule. The conversion of anthra- 
cene into dianthracene under the 
action of near-ultraviolet light is a 
well-known fact, and Weigert has 
shown that, in this case, dimerization 
and quenching of fluorescence are 
complementary (1799). 

With respect to the self-quench- 
ing of anthracene and other ar- 
omatic hydrocarbons, however, statements are found in the literature 
which seem to be completely contradictory. According to different 
authors the self-quenching of anthracene in benzene, hexane, and 
other solvents is very pronounced (Table 66). According to Pekerman 
the fluorescence of anthracene dissolved in benzene shows typical self- 
quenching, while this phenomenon is completely lacking in alcoholic 
solutions in the concentration range from 10 -6 to 2-10 -2 g per cc 
(1201b). 

The figures of Table 66 A are taken from a paper by Bo wen, the 
value of k s for anthracene in benzene being in complete agreement 
with that found by another author (144,1291). The relatively great 
difference of the corresponding value in Table 66B (after Weil-Malherbe 
and Weiss) cannot well be ascribed to the strong prequenching by 



20 40 60 

TEMPERATURE 



'C. 



Fig. 122. Influence of tempera- 
ture on the self-quenching of 
fluorescein in aqueous solutions 
(Levshin). 
Concentration c in g per cc. 



POLYMERIZATION AND SELF-QUENCHING 



35? 



Table 66 

Quantum Yield Q and Self-quenching Constant k s of Aromatic 

Hydrocarbons in Solution Excited by Near u.v. 

A. Anthracene in the Presence of Atmospheric Air 
(Concentration range : 1.8-1 (r 3 -4. 5 • 1 (T 2 ) 



Solvent 


Benzene 


Hexane 


Acetone 


Biacetyl ether 


Paraffin 




21.5 
26 


23 
90 


21 
53 


21.4 
75 


29 
3 



B. Various Hydrocarbons in the Absence of O a [1806) 
(Concentration range: 10 _5 -10 -2 ) 



Compound 


Solvent 


*s 


Compound 


Solvent 


"s 


Anthracene 


Benzene 


60 


Pyrene 


Benzene 


< 10 


Anthracene 


Hexane 


100 


1,2,5,6-Dibenz- 






3, 4-Benzopyrene 


Benzene 


70 


anthracene 


Benzene 


20 


9,10-Dimethyl- 






Methylchol- 






1,2-benz- 






anthrene 


Benzene 


77 


anthracene 


Benzene 


83 


Ethylchloro- 


Ethan ol 


10 5 


1,2-Benz- 






phyllide 






anthracene 


Benzene 


40 









2 in the first case, since the solubility of oxygen is much smaller in 
benzene than in hexane. According to a later paper by Bowen, the 
self-quenching constant k s for benzene, anthracene, and all other 
hydrocarbons enumerated in Table 61 A (Section 108) is smaller than 
0.5, when the solutions in oxygen-free hexane are excited by the 
mercury line 2537A. Moreover, under these conditions the much 
higher value of Q = 46 % (instead of 23 %) was obtained for he 
fluorescence yield of anthracene. The discrepancy in the values of Q 
might perhaps be explained by the smaller depth in which the exciting 
radiation of wavelength 2537A is completely absorbed and by a corre- 
sponding difference in the reabsorption of the fluorescence radiation. 
It was pointed out in Section 105, however, that this explanation 
cannot be applied to the disagreement between the k s values. In the 
case of anthracene, Bowen 's later data refer to so low a concentration 
range (from 0.7 to 2.8- lO -4 ), that they may still correspond to the 
horizontal branch of the yield curve (Figure 125). It is doubtful how 
far this consideration can be extended to the other compounds listed 
in Table 61A (146,1806). 

While no quantitative data are available for the self-quenching 

Pringsheim 13 



358 CONDENSED SYSTEMS 

of benzene in alcohol, it has been stated by various investigators that 
the fluorescence strength at first increases with concentration, then 
reaches a maximum at a volume concentration of about 2 % (corre- 
sponding to 2.3- 10~ 2 mole per liter), and finally drops almost to zero 
in pure liquid benzene. The fluorescence reappears strongly when the 
liquid crystallizes (1350). 

The fluorescence yield of dyes becomes smaller also at high con- 
centrations, when they are dissolved in a solid ; for instance, in sugar 
the Q-value of uranin is constant at concentrations between 10~ 5 and 
10 - *, it drops rapidly at concentrations above 10 -4 , and is only about 
7 % of its highest value at the concentration of 2- 10~ 2 .* In media of 
such great viscosity, no collisions occur and dimerization due to the 
interaction of an excited and an unexcited molecule is possible only if 
the two are immediate neighbors. Otherwise, self-quenching in a solid 
solution must be ascribed either to "configuration-quenching" or to 
the production of dimers by a dark reaction preceding the solidifi- 
cation of the solution. The latter phenomenon alone would not suffice, 
however, for an interpretation of Levshin's observation that the dura- 
tion of the phosphorescence of fluorescein in boric acid is reduced to 
about one-half when the concentration of the dye is increased from 
10~ 2 to 3-10- lo / o (92T). 

All the foregoing remarks refer to directly excited fluorescence 
and phosphorescence of solutions, as it is observed, in general, at room 
temperature. G. N. Lewis found the duration of the indirectly excited 
slow fluorescence of fluorescein in glycerol at — 180° C to be inde- 
pendent of the dye concentration in the range from 5- 10 -6 to 5- 10~ 2 
moles per liter. It is not impossible that, nevertheless, the apparent 
yield is appreciably smaller at the higher concentrations if its decrease 
were due exclusively to the formation of nonluminescent dimers (g2g, 

93o). 

If the concentration of a dye in aqueous solution is just below the 
critical value c of Table 63, the quenching efficiency of foreign ions, 
such as I - and Br~, is much larger than in solutions of lower dye 
concentration. Moreover, the £>-band appears in the absorption 
spectrum under these conditions when the quencher is added to the 
solution. Both effects become weaker with increasing temperature. 
Banow supposes, therefore, that, because of the tendency of the halide 
ions to hydration, the number of solvent molecules at the disposal of 
each dye molecule is lessened and thus the "real concentration" of 

* These concentrations are given in gram dye per cc solvent (Table 62). 



POLYMERS WITH NEW FLUORESCENCE BANDS 



359 



5727 A 

P 
i 



8000 



4000 



the dye is increased. It would be a first step toward salting out. 
Similar effects are not observed at the same concentration in alcoholic 
solutions in which no polymerization takes place. In these solutions, 
an increase in temperature enhances the quenching by foreign ions 
as in the other instances described in Section 107 (60,1723 a). 

115. Polymers with New Fluorescence Bands. There is, of course, no 
reason in principle why polymerized molecules should always be non- 
fluorescent. Pseudoisocyanine chloride exhibits relatively broad and 
diffuse "molecular" absorption bands M 1 at 5300A and M 2 at 4820A 
in alcoholic solutions and if the concentration is low, also in aqueous 
solutions. If dye concentration 
exceeds 10~ 3 molar in aq. soluti- 
on, a new narrow absorption 
band P appears in the yellow, 
and, simultaneously, a weak 
fluorescence. By increasing the 
concentration to about 10"" 2 
molar, the fluorescence and 
absorption band P are greatly 
enhanced, the absorption in the 
other bands becomes weaker, 
and the liquid solution is con- 
verted into a gel (Figure 123). 
If the temperature is lowered, 
the P-band in the absorption 
spectrum and the fluorescence 
begin to be observable at lower 
dye concentrations. The pheno- 
menon as a whole is caused by the formation of highly polymerized 
molecules which consist of large numbers of parallel planar dye 
molecules piled upon each other face to face so that long chains are 
built up [685,1414-1418). 

The fluorescence of these solutions is exceedingly sensitive to the 
presence of quenchers of very low relative concentrations. Addition 
of 10- 5 mole per liter of pyrocatechol to a solution containing 0.2 mole 
per liter of pseudoisocyanine chloride quenches the fluorescence to 
80 % of its maximum value : a single quenching molecule is able to 
affect the light emission originating from a very large number of dye 
molecules which obviously form a unit. The molar concentration of the 
polymers is far below the calculated concentration of the non- 
associated dye molecules and the light emission by the entire poly- 



- 




5297 A . 




- 




1> 


4819 A 


"J 




1 


1 



1800 



2000 



Fig. 123. Molar absorption coeffi- 
cients of y-isocyanm 6 chloride in 
aqueous solution (Scheibe). 
1: 10- 4 mole per liter. 2: 10- 2 . 



360 CONDENSED SYSTEMS 

merized molecule is inhibited if any of the dye molecules forming the 
chain are in contact with a quenching molecule. 

Various cyanine dyes behave similarly. For the dye mentioned 
above, the wavelength of the P-band is 7287A and the center of the 
fluorescence band which overlaps the P-band is shifted only slightly 
toward greater wavelengths. The fluorescence can be excited as 
"resonance radiation" by light absorption in the P-band or by ab- 
sorption in one of the other bands which are characteristic also of the 
nonpolymerized molecules ("molecular bands"). The fluorescence 
yield rises rapidly in the concentration range in which the gelation 
occurs and remains constant at higer concentrations up to the point 
at which only very little water is left in the solution. With complete 
dehydration the P-band and the corresponding fluorescence disappear. 
The pure crystalline dye shows a deep red fluorescence. 

The exact location af the P-band depends on the amount of water 
which is present in the gel. The water molecules play an important part 
in the cementing of the polymerized aggregates. In alcoholic solutions 
no polymerization of this kind occurs, the P-band does not appear in 
the absorption spectrum and the solution is not fluorescent at any dye 
concentration {339,989a). 

Different dyes of this class have P-bands more or less shifted in 
wavelength with regard to each other. In a mixture of two such dyes 
— for instance, diethyl-^-cyanine and diethyl-^-thiacyanine which 
have individual P-bands at 5790 and 5450A — the dyes together 
form "heteropolymerized" molecules with a P-band which is 
intermediate between the bands of the two isolated dyes and 
cannot be explained by a mere superposition of the two individual 
bands. 

In solutions of dinaphtho-substituted ^r-isocyanine, the P-band 
appears in the absorption spectrum at dye concentrations about 100 
times smaller than in the solutions of the other dyes; the solution, 
however, does not turn into a gel, nor does it become fluorescent. Only 
the high degree of polymerization at which the solution is solidified 
brings about the fluorescence. The less complete polymerization by 
which the solution is not converted into a gel does not suffice, though it 
is sufficient for the appearance of a P-band. 

On the other hand, some dyes of similar structure become gels 
at high concentration in aqueous solution without the appearance of a 
new narrow absorption band; nevertheless, they too become fluo- 
rescent in the gel state, although they are not fluorescent as long as the 
solution is liquid. Thus, the highly polymerized molecules of mono- 



FLUORESCENCE OF NEUTRAL AND IONIZED MOLECULES 361 

naphtho-^-thiacyanine can be excited to a green fluorescence by 
irradiation with near-ultraviolet light (732). 

Instead of increasing the concentration of an aqueous solution, the 
fluorescent dye polymers can also be "salted out" by addition of 
hydrochloric acid to a dilute solution. 

E. Fluorescence and Ionization 

116. Fluorescence of Neutral aud Ionized Molecules. The decrease 
of fluorescence yield with increasing concentration was first observed 
in aqueous dye solutions, and it seemed very plausible to assume that 
the effect was due to the decreasing dissociation of the molecules into 
ions. The controversy regarding the question of whether dyes are 
fluorescent only as ions, occupies much space in the earlier fluorescence 
literature. The discovery of the strong fluorescence of pure aromatic 
hydrocarbons, such as anthracene or naphthacene, which never 
ionize in solutions, proved unequivocally that this could not be a 
general rule. These hydrocarbons show self-quenching of the same 
magnitude as do the dye solutions. 

There is no reason why fluorescence power should be essentially 
connected with the state of ionization of a molecule. It is possible that 
a compound is fluorescent both in the neutral state and in different 
states of ionization, but each of these states will, in general, be charac- 
terized by different absorption and emission bands. Thus, the blue- 
violet fluorescence of quinine sulfate in aqueous solution is relatively 
weak ; if the solution is acidified, the color of the fluorescence changes 
into a whitish blue and the fluorescence intensity is greatly enhanced. 
This enhancement is not caused primarily by an increased fluorescence 
yield but by a corresponding increase in absorption power in the near 
ultraviolet. In an alkaline solution the fluorescence is still weaker than 
in neutral solution and of a dark violet color. Different ionization 
states of the quinine sulfate molecule with unequal optical properties 
coexist in a solution in proportions depending on the pH. If the 
whitish blue fluorescence of an acidified aqueous solution is quenched 
by the addition of KI, the fluorescence color turns into the blue-violet 
characteristic of the neutral solution, because the doubly charged ions 
responsible for the whitish-blue fluorescence are more strongly 
quenched than the others.* If, on the other hand, quinine sulfate is 

* If an aqueous solution of quinine sulfate is acidified by addition of a very 
small quantity of hydrochloric acid, the well-known light blue fluorescence 
appears ; increasing the CI - concentration quenches this fluorescence completely, 
so that even in the acid solution only a weak, violet fluorescence is left. 



362 



CONDENSED SYSTEMS 




absorbed from an acidified or from a neutral solution on to silica gel, 
the absorbed material always shows the same light blue fluorescence, 
because the doubly charged ions are preferentially absorbed on the gel 
(982, unpublished experiments). 

The behavior of fluorescein in solutions of varying pH is similar. 
The negative ions, prevailing in alkaline solutions, show a brilliant 
yellow-green fluorescence ; the fluorescence of the positive ions formed 
in an acidified solution is blue green and weaker than the former when 
excited by near-ultraviolet radiation (71). This decrease in fluo- 
rescence power is again due at least 
in part, to a smaller absorbing 
power; if excited by light of wave- 
lengths below 3000A the difference 
in fluorescence intensity of the 
alkaline and of the acidified solutions 
is much less pronounced. In neutral 
solutions fluorescein is almost color- 
less and nonfluorescent. 

Quinoline red has a very nearly 
constant fluorescence yield in the 
whole pH range from — 1 to +12 
(339) • Other dyes — for instance, 
alloxazine and its derivatives (among 
which riboflavin or vitamin B 2 is 
the most interesting) — are fluores- 
cent only in solution of medium pH 
(between 3 and 9), where they probably exist as neutral molecules 
or as amphoteric ions (7 32, 846). The positive or negative ions formed 
in strongly acidified or alkaline solutions are not fluorescent (Fig. 124). 
3-Aminonaphthalhydrazide (luminol) is adsorbed from an alcoholic 
solution on gels of either polarity, and in both cases the adsorbed 
substance has the same strong blue fluorescence characteristic of the 
amphoteric -molecule, which is bound to either gel by one of its 
localized charges. In alkaline or acidified solutions the compound 
exists in the form of a negative or a positive ion; the fluorescence 
of the latter is green, even when adsorbed on a gel of negative polarity, 
and the former is not fluorescent at all. 

Because of the diffuseness of most fluorescence bands, the 
weakening of one band and the simultaneously increasing intensity of 
another with changing pH of a solution frequently gives the impression 
of a continuous transition from one spectrum to the other by a stepwise 



Fig. 124. Fluorescence intensity 
of riboflavin and alloxazine as 
a function of pH (Kuhn and 
Maruzzi, Karrer and Fritsche). 

1 : riboflavin. 2 : alloxazine 

viewed through blue screen. 

3: same viewed through 

green screen. 



FLUORESCENCE AND PHOTOELECTRIC EFFECT 363 

shift of the band maximum. This, however, is never the true behavior. 
The fluorescence spectrum of acridine at room temperature consists of 
a broad band which has its maximum in the blue violet in a neutral 
solution and in the blue green in an acidified solution. At liquid-air 
temperature both bands split up into four narrow bands which overlap 
only very little. If, under these circumstances, a neutral alcoholic 
solution is acidified very slightly, it can easily be seen that the new 
band system appears gradually while the other bands become weaker 
(unpublished observations) {1469). If thin layers of acridine and an 
organic acid, such as salicylic acid, are distilled in vacuo, one on top 
of the other, onto a cold surface and are maintained at the tempera- 
ture of liquid air, the color of the vio'et fluorescence which is excited 
by irradiation with the near u.v. light of a mercury lamp changes, 
with time, to green; the same reaction of the acridine molecule which 
occurs spontaneously in an acidified liquid solution and which consists 
in the capture of a proton is induced in the solid state by the absorption 
of light. The process is reversed by a subsequent irradiation with the 
mercury line 2537A by which the fluorescence regains its initial violet 
color (1640a). 

If the characteristic fluorescence of a solution is due to the fact 
that it contains a compound in a certain state of ionization — for 
instance, doubly charged quinine ions — the observed strength of the 
fluorescence must, of course, depend on the degree of ionization 
which is a function of concentration of the compound. However, a 
strict proportionality between the degree of ionization and the fluo- 
rescence intensity would occur only under especially favorable con- 
ditions; the fluorescence strength at low concentrations would be 
proportional to the number of ionized molecules only if the non- 
dissociated ions have no absorbing power for the exciting radiation, 
and the fluorescence yield would be proportional to the number of 
ionized molecules only if ionized and nonionized molecules have 
exactly the same absorbing power for the exciting light (345). 

Under no circumstances can the whole problem of self-quenching 
be explained by the influence of the concentration on ionization. This 
was shown by Vavilov's measurements, in which the influences of the 
concentration on the fluorescence yield Q and the electric conductivity 
a were compared for uranin solutions. In the concentration range where 
the steep slope of the yield curve sets in, the conductivity curve shows 
no anomaly whatsoever, its shape over the whole range being typical 
for a strong electrolyte.* (Figure 125) (1749). 

* The very steep slope of the conductivity curve obtained by Vavilov for 



364 



CONDENSED SYSTEMS 



Because of the dependence of the color and intensity of the 
fluorescence of many solutions on their pH, such solutions can be 
used as "indicators," in the same way as the well-known color indi- 
cators. Lists of fluorescent indicators for a pli range from to 13 have 
been compiled by several authors. 

117. Fluorescence and Photoelectric Effect. The question of 
whether neutral molecules or ions are the carriers of photoluminescence 
bears no relation to the problem of the mechanism by which lumi- 
nescence is produced. It would be different if the excitation of fluo- 



1.0 

0.8 

0.6 

<S 04 

0.2 



V 








\ 










\ \ 

* \ 








- 


■V3 

--< 


'--it 


V^-^ 






1 




1 


1 


1 



100 

80 

60 
a 

40 
20 



8 16 24 X I0" 3 

CONCENTRATION in g/cc 

Fig. 125. Fluorescence yield and electric conductivity of 

an aqueous fluorescein solution as a function of the dye 

concentration (Vavilov) . 

a : fluorescence yield O/O . b : electric conductivity a. 

rescence were due to the ionization process itself, as was assumed by 
different authors for some time. A probable connection between photo- 
electric sensitivity and fluorescence power was pointed out for the 
first time by Elster and Geitel, who found that certain fluorescent 
minerals as well as artificial "phosphors" showed a relatively strong 
photoelectric emission when they were irradiated with light which was 
able to excite their luminescence. Starting from this observation, 
Lenard later developed his photoelectric theory of the phosphorescence 
of crystal phosphors (compare Chapter VII) (361). 

Others, especially J. Stark, tried to apply the same hypothesis to 
fluorescent dyes and other organic compounds. As a matter of fact, 
he observed photoelectric emission by dyestuffs in the solid state under 

the lowest dye concentrations must be due to some secondary cause; an equi- 
valent conductivity of 600 is quite impossible for a dye ion of molecular weight 
278 in an aqueous solution. 



FLUORESCENCE AND PHOTOELECTRIC EFFECT 365 

the action of light which was able to produce the fluorescence of the 
same dyes in a liquid solution. However, the solid dyes were not fluo- 
rescent and no photoelectric effect could be produced in any liquid 
solution. Results which at first were supposed to prove the existence 
of the effect looked for were soon proved to be erroneous ; they were 
really due to thin colloidal layers of the solid dye formed on the surface 
of the solution. Nor is an increase of electrical conductivity of the 
solutions produced as an internal photoelectric effect, as was shown 
by Goldmann, whose possible experimental errors were less than 
0.01 %. Some apparently positive results of other authors are ex- 
plained in part by an increase of temperature and in part by a polari- 
zation of the electrodes (so-called Becquerel effect). It is true that, 
according to Volmer, solutions of aromatic hydrocarbons are ionized 
by irradiation with light of wavelengths below 2200A, but Volmer 
showed also that light of longer wavelengths which excited strong 
fluorescence in these solutions had no influence on their electric con- 
ductivity. It need not be emphasized that the hypothesis according to 
which a dye in solution should be ionized by light absorbed in its 
long-wavelength absorption band has lost all theoretical foundation 
{510,1199,1549,1552, T779) . 

The problem with regard to organic compounds in the solid 
crystalline state is somewhat different. Volmer found that light of the 
violet and near-ultraviolet region which excites fluorescence in solid 
anthracene also causes photoconductivity in the crystals. On the other 
hand, it has already been mentioned that light which is absorbed in the 
typical anthracene bands between 3500 and 3900A is able to excite the 
fluorescence of naphthacene dissolved at a very low concentration in 
the anthracene crystals. Similar cases of a "sensitized fluorescence" 
were observed when naphthacene is dissolved in different other crys- 
talline hydrocarbons. It is certain that the very characteristic strong 
green fluorescence of naphthacene is not excited by the absorption of 
light by the relatively few naphthacene molecules themselves. If 
crystals in which the violet anthracene fluorescence is almost com- 
pletely suppressed by the green naphthacene luminescence are heated 
to the melting point, the green luminescence vanishes at the instant 
at which the substance is liquified. If at room temperature the same 
crystals are dissolved in liquid benzene the fluorescence spectrum of 
the solution consists exclusively of the anthracene bands with no trace 
of the napthacene bands, although the relative number of anthracene 
and naphthacene molecules remains unchanged (i43b,458a,i8oj, un- 
published observations). 



366 CONDENSED SYSTEMS 

It might be that the primary effect of light absorption in the 
crystals is the liberation of photoelectrons, and that these transfer 
the excitation energy through the crystal to a naphthacene molecule, 
which has a greater emission probability than the anthracene mole- 
cules. However, this mechanism, although it plays a very important 
part in the luminescence of "crystal phosphors," can hardly be sup- 
posed to act in anthracene crystals. The absorption bands of these 
crystals have — except for a small shift towards greater wavelengths 
— exactly the same structure as the absorption bands of anthracene 
vapor or anthracene in liquid solutions, and so they cannot be ascribed 
to the transition of an electron to a free conduction band in the crystal : 
they must be associated with an electronic transition within the mole- 
cule itself. (The same is true for the uranyl salts and other fluorescent 
crystals which do not belong to the class of crystal phosphors). 

The correct interpretation of the phenomena is probably to 
ascribe it to exciton migration, but the experimental material is not 
yet sufficient to draw unequivocal conclusions. It may be mentioned 
in this connection that, according to Franck and Teller, the narrow 
absorption and fluorescence bands of polymerized cyanine dyes are 
caused by exciton migration along the chains of which the polymers 
consist. However, there are reasons which make it at least equally 
probable that the bands are due instead, to an electronic vibration 
moving from one end of the chain to the other (428). 

Taking everything into account, it can be stated that photo- 
electric effects have no, or only a very unimportant, part in the photo- 
luminescence phenomena with which this chapter is concerned. 



F. Polarization and Angular Intensity Distribution 
of Fluorescence Radiation 



118. Polarization Caused by the Anisotropy of Oscillators. If a 

totally isotropic electronic oscillator is excited by the absorption of 
plane-polarized light, the radiation emitted by the oscillator is also 
plane polarized. However, this polarization is affected by very small 
perturbations such as magnetic fields, interaction with other molecules, 
etc.; in a condensed system it would, in general, be completely 
destroyed. If, nevertheless, fluorescence radiation from a condensed 
system is partially polarized, this can be due only to the fact that the 



POLARIZATION CAUSED BY ANISOTROPY OF OSCILLATORS 367 

molecules as a whole are more or less optically anisotropic and that 
there are fixed axes within the molecules along which the electronic 
oscillations occur preferentially. 

In solid dye solutions the fluorescence and phosphorescence was 
found to be polarized to nearly the same degree (209). It is quite im- 
possible that an isotropic electronic oscillator should "remember" for 
a period of several seconds the direction of the impulse which it 
received at the moment of excitation, and this observation proved for 
the first time that the polarization was due to the orientation of the 
whole molecules and to the persistence of this orientation.* 

A temporary dichroism, which is produced in a solid dye solution 
when it is irradiated with plane-polarized light of great intensity, is 
complementary to the polarization of the afterglow. If, in Lewis' ex- 
periments described in Section 104, the "exciting" light beam is 
polarized with its electric vector parallel to the Z-axis, the absorption 
of the "measuring light" in the band at 4365A which originates from 
the ground state N of the fluorescein molecules is about 30 % weaker 
for light with its electric vector parallel to Z than for light with its 
electric vector perpendicular to Z. On the other hand, the light ab- 
sorption in the band at 6500A due to the molecules in the quasi-stable 
state M is more than 50 % weaker for light polarized parallel to Z. 
This proves once more the anisotropy of the individual molecules. 
Those molecules which are oriented so that their electric oscillators 
have a strong component parallel to Z are preferentially removed 
from the ground state and raised into the quasi-stable state by the 
strong illumination with polarized light (930). 

Although the fluorescence of a dye solution is partially polarized 
when it is excited by plane-polarized light, it shows no trace of circular 
or elliptical polarization when the exciting light is polarized circularly 
or elliptically. If electrons within the molecules were free to follow the 
direction of the electric field which is produced by the incident ra- 
diation, circular or elliptical polarization should be observed under 
these conditions, as in the resonance radiation of vapors (528,1044, 
1223). 

In Section 72 the problem of the totally anisotropic (linear) 
resonator as a source of emission and absorption has been mentioned. 

* According to later investigations, the degree of polarization of the 
phosphorescence is usually smaller by a few per cent than the polarization of 
the fluorescence. This is understood without difficulty, however, since all 
depolarizing effects which will be mentioned in the following sections increase 
with increasing duration of the emission process. 



368 CONDENSED SYSTEMS 

The assumption of the presence of such oscillators does not suffice to 
represent many experimental results obtained with, complicated mole- 
cules in condensed systems. The most general model of a fluorescent 
molecule consists of an emitting oscillator F and an absorbing oscil- 
lator A which have different frequencies but are coupled to each other 
so that light absorbed in A is re-emitted by F. F has different am- 
plitudes a lt a 2 , a 3 along three axes f , -q, £ fixed within the molecule 
and A has different amplitudes a' v a 2 , a 3 along three axes f ', rj', £' 
which are rotated with respect to £, rj, £ by angles with the cosines fin 
(i = 1, 2, 3; j = 1, 2, 3). In the following it may be assumed that a 3 
(parallel to £) is larger than a x and « 2 > an ^ that a 3 (parallel to £') is 
larger than a 2 and a' v If all fy = for i =£ j and the ft,- = 1, F and A 
coincide; if, furthermore, a x = a 2 = 0, the model goes over into the 
totally anisotropic oscillator. In general, F and A will coincide if the 
emission and absorption processes correspond to the same electronic 
transition. If, however, the absorption occurs in an absorption band 
which corresponds to an electronic transition other than the emission 
band, A and F may form any angle less than, or equal to, 90° with 
each other (668,671). 

If the fluorescence spectrum consists of one single band, the 
degree of polarization is the same for all parts of this band. Only in the 
infrequent cases where a- fluorescence band is split up into many 
narrow lines, as in the crystalline uranyl salts, can groups of these lines 
show a different degree of polarization (ordinary and extraordinary 
spectrum). If the structure is blurred out — for instance, at higher 
temperatures — only the average polarization of the whole band 
remains to be measured. 

A classical model does not exist for an oscillator with a single 
frequency, which is anisotropic in three perpendicular directions.* 
The well-known Langevin molecule, in which an electron is bound in 
three perpendicular directions by different forces, also has three 
different characteristic frequencies. This has little importance in the 
treatment of Rayleigh-scattering, where the frequency of the incident 
light differs widely from the characteristic frequencies of the scattering 
molecules. According to quantum theory, the model would correspond 
to a molecule with three excited levels of practically identical energy 
but of different transition probabilities to the ground level; each of 

* Such a model might be realized by assuming an oscillator which is 
spherically symmetrical as far as the binding forces are concerned, but in which 
a trigger mechanism inhibits the oscillations along two of the axes»j and £ during 
certain periods. 



POLARIZATION CAUSED BY ANISOTROPY OF OSCILLATORS 369 

these transitions would produce radiation polarized parallel to one of 
the axes f , 17, £. A quantum-mechanical treatment of the problem has 
not yet been put forward. Jablonski's calculations are purely for- 
malistic and were derived from the assumptions stated above. 

Whatever may be the absorption process, the same equilibrium 
distribution between the different excited levels (or excited oscillators) 
is always restored before the emission process sets in in a condensed 
system. Hence, the polarization of the fluorescence emitted by an 
individual molecule is exclusively determined by the properties of the 
molecule and by its orientation with respect to the observer, and not 
by its orientation with respect to the direction and polarization of the 
primary light. 

In the following discussion the exciting light beam is supposed to 
be parallel to the X-axis and to be plane polarized with its electric 
vector parallel to the Z-axis* The fluorescence light is observed in the 
direction of the Y-axis, X, Y, Z being a system of orthogonal coordi- 
nates fixed in space. The orientation of the molecules, or of their 
f ', rj', £' system with respect to the Z-axis, is important only for the 
intensity of excitation (or for the probability of excitation) of an 
individual molecule, and, therefore, it determines the intensity of the 
fluorescence radiation. 

The polarization of the fluorescence can be negative, or the fluo- 
rescence light can be partially polarized perpendicularly with respect 
to the electric vector of the exciting light (perpendicular to Z), if the 
angle (££') is greater than 54.5° (($&< Ijy/z). Strong negative polari- 
zation of great intensity occurs if £' is parallel to Z and perpendicular 
to £. The polarization of the total fluorescence radiation, as it is 
measured by an observer, results from the superposition of the inco- 
herent elementary waves emitted by all excited molecules. It is there- 
fore determined by the orientation of all molecules, with respect to 
the observer as well as to the electric vector of the exciting light. Two 
limiting cases are of special interest for the angular distribution of the 
individual oscillators relative to each other : complete order or paral- 
lelism of all systems i, 7), £ and f ', 17 ', £', respectively, as in a crystal- 
line lattice and complete statistical disorder as in a liquid solution. 
Intermediate instances of a partial order can be realized in streaming 
liquids or with compounds adsorbed on an anisotropic gel. 



* If the exciting light is unpolarized, and if the fluorescence is observed in 
any direction perpendicular to the primary beam, the equation in the footnote 
of Section 72 again determines the relation between pp and p n . 



370 CONDENSED SYSTEMS 

119. Polarization of Fluorescence in Liquid Solutions and Influence 
of Molecular Rotation. If the fluorescing molecules can be represented 
by linear (completely anisotropic) oscillators, if they are at rest, and 
if they have a statistical angular distribution, the polarization of their 
fluorescence radiation is, under the conditions stated in the last 
section, p = 0.5 (50%). For the more general model with arbitrary 
values of all amplitudes a t and a' (i '■ = 1, 2, 3 and j = 1, 2, 3) and 
arbitrary values of the directional cosines fty, the equation for the 
degree of polarization takes the form : 

3yS a — 1 

i 

where fP = 2^^^. The extreme values of p are — 1 / 3 and + 1 / 2 , the 

3 

maximum negative polarization corresponding to /S 2 = and the 
maximum positive polarization to jS 2 = 1. (For both extreme cases, 
a i = a 2 = a i = a 2 = ; #3 and «3 > 0, and j8 33 = or = 1 , respectively) 
(611,672). 

In a vapor at low pressure the angular orientation of the axis 
around which the molecules rotate, in general remains, constant 
during the lifetime of an excited state. Under these circumstances, 
the fluorescence emitted by linear oscillators which are excited by 
plane-polarized light is depolarized from p = 50% to p = 14.3%, 
because of the molecular rotation. In a liquid solution, however, the 
molecules no longer perform the rotation characteristic of a free- 
spinning top: their rotation is determined by the laws of Brownian 
movement (gog, 1217,1220). 

According to the theory developed by Smoluchowski and by Ein- 
stein, a spherical particle of volume V rotates in a liquid of viscosity 17 
in a short time At through an angle Ay, the mean value of which is: 



RT 

TjV' 



a y = i~^- At < 80 > 



By inserting the sufficiently short lifetime r for At in this equation, 
the reduced degree of polarization which results from rotations of all 
individual resonators around statistically oriented axes can be calcu- 
lated to be : l 

P =Po £y- (8ia) 

If all other parameters occurring in Equation (81a) are known, 
the measurement of p as a function of 77 and T permits the deter- 



POLARIZATION OF FLUORESCENCE IN LIQUID SOLUTIONS 37 1 

mination of t, exactly as the lifetime of an excited mercury atom was 
derived from the depolarization of its resonance radiation in a mag- 
netic field, t is supposed to be a constant in Equation (81a) and 
therefore it cannot be claimed as a new result that, in the range of 
validity of Equation (81a), t is independent of the viscosity: if t is a 
function of 77, the equation cannot be applied (224). 

Since, for small viscosities, p is proportional to the viscosity it 
can easily be understood, in view of the small viscosity of the usual 
solvents (water, alcohol, hexane, etc.), why the fluorescence of liquid 
solutions was generally considered to be always unpolarized. The ob- 
servation that fluorescence emanating under an oblique angle from 
a transparent medium is partially polarized is, of course, not related to 
this problem. It follows from Fresnel's laws governing the reflection 
of light on the surface which separates the fluorescing medium from 
the surrounding atmosphere. The degree of polarization found under 
these conditions agrees quantitatively with the value derived from 
Fresnel's equations. For the fluorescence of canary glass observed 
under an angle of 80°, p becomes about 35 %. In order to avoid this 
secondary effect, observations must be made as nearly perpendicular 
to the surface as possible (1030). 

Only by investigating the fluorescence of dyes dissolved in highly 
viscous media, such as glycerol or gelatin, did Weigert discover that 
the earlier assumption was erroneous (1800,1804). Further research 
on the polarization of the fluorescence of dyes, hydrocarbons, cy- 
anoplatinites, and uranyl salts in liquid solutions and its dependence 
on the different parameters contained in Equation (81a) proved that 
the theoretical ideas stated in the last section were in general agreement 
with experimental results. In Table 67 a number of examples of the 
interdependence of p and ij are compiled. The viscosity was varied 
either by stepwise addition of water to glycerol or of ether to isobutyl 
alcohol, by using a series of solvents which, apart from their different 
viscosity, have similar properties (for instance, the different aliphatic 
alcohols), or, finally, by varying the temperature of a solution (197, 
219,567,909,910,1043,1765). In the last case not only the variation of 
■q but also that of T must be taken into account, as is shown by the 
comparison of the two curves in Figure 126. 

Equation (81a) can be written in the form: 

(i/P - Vs) = WPo - V.) (i + ^ t) < 81b > 

Hence, \jp as a function of I/17 is represented by a straight line which 



372 

20 
10 



y/eT 


itV^- 




1 


1 





20 
7) XlO 3 



40 



CONDENSED SYSTEMS 



40 



Fig. 126. Polarization of 
fluorescence of erythrosin 
in various alcohols as a 
function of the viscosity 
[Levshin (gog)] 



*«, 



bl 

T ; 

T /* -J * "*^ 



50 



100 



I/77 



150 



Fig. 127. Polarization of fluorescence as 

a function of the viscosity (Pringsheim 

and Vogels). 

a : trypaflavine in octanol-ether. b : try- 
paflavine in glycerol-water. c: fluores- 
cein in glycerol-water (after F. Perrin). 



Table 67 

Degree of Polarization p of the Fluorescence of Liquid 
Solutions as a Function of the Viscosity r) 



Uranin in 

glycerol + 

water 


V 


0.01 


0.018 


0.033 


0.055 


0.137 


0.348 


3.82 j 00 ( Po ) 


P 


1.7 


3.0 


5.9 


10.5 


19.2 


29.2 


42 


(44) 



Trypaflavine 

in octanol 

+ ether 


V 


0.08 


0.09 


0.12 


0.15 


0.27 | 0.37 


0.67 


00 (Po) 


P 


3.1 


3.5 


4.3 


5.3 


6.7 


8.3 | 10 


(35) 



Erythrosin in : 




Methanol 


Ethanol 


Propanol 


Isobutanol 


Glycerol 


Water 




n 


0.006 


0.012 


0.024 


0.042 


6 


0.011 




p 


6.5 


10.4 


14.4 


17.6 


35 


32 





Tempera- 
ture ° C 


15 


31 


47 


63 


81 


Erythrosin 
in water 


>/ 


0.0114 


0.0079 


0.0058 


0.0045 


0.0035 


P 


32 


28 


24 


20 


15 



crosses the axis of I/77 =0 (corresponding to infinite viscosity) at the 
point p = p . The value of p is found by extrapolation from a series of 



POLARIZATION OF FLUORESCENCE IN LIQUID SOLUTIONS 373 

measurements of p in solvents of increasing viscosity; from p the 
lifetime t can be calculated, f 

In order to derive values for t from his measurements, Levshin 
introduced plausible values for V in Equation (81a) and in this way 
obtained lifetimes which were in reasonable agreement with those 
found by means of a fluorometer. Later, F. Perrin determined the V's 
for different dyestuffs in each individual solution by diffusion measure- 
ments. The value of V in Equation (81a) is not the volume of the 
isolated dye molecule, but the volume of the molecule with its solva- 
tion envelope, so that V differs for a given dye in different solvents — 
for instance, it is not the same in pure glycerol as in a glycerol-water 
mixture. Therefore, not l/^but I/17 V must be used as the variable in the 
diagram for l/p. In the range of not too small viscosities, at least, 
Perrin obtained points lying fairly well on a straight line (Fig. 127) and 
from these he was able to calculate values for p and for t which are 
reproduced in Table 68 {gog,gio,i2iy, 1220,1221,1223,1226,1765). 

Table 68 

Maximum Polarization p and Lifetime t of Excited 

State for Fluorescent Solutions 



Fluorescent 
compound 


Uranin 


Erythrosin 


Resorufin 


Chloro- 
phyll 


Quinine 
sulfate 


Anthra- 
cene 


Cyanopla- 
tinite 


A. • • • • 
t-10 9 . . . 


44 
4.3 


45 
0.08 


44 
3.1 


43 

30 


46 
40 


25* 
250 


40 
0.3 



* For a much higher value of p , compare page 374. 



However, the theory as developed by Levshin and by Perrin is 
not yet quite satisfactory. Not only is the hypothesis that the molecules 
can be treated as ideal spheres, as in the theory of Smoluchowski and 
Einstein, a rather rough approximation but moreover, the values of 
t cannot'be assumed, in general, to be the same in solutions of differ- 
ent viscosities, as has been pointed out in Section 107. It would be 
preferable, therefore, to take TQ r /-qV instead of T/rjV as variable in 
diagrams of the type of Figure 126. 

For rhodamine B or G dissolved in glycerol at a concentration 
of 5- 10~ 4 g/cc, the degree of polarization of the fluorescence does not 

f t can be directly derived from the diagram by prolonging the straight 
line beyond the zero axis to the point \\p = 1 / 3 and a corresponding negative 
viscosity rj- This point rj < and p = 3 has no physical meaning, since neither 
negative viscosities nor polarizations greater than 100 % can exist. The lifetime 
is given by : T = — rjV j RT. See, for instance, curve a in Figure 127. 



374 CONDENSED SYSTEMS 

decrease at all with increasing temperature and decreasing viscosity, 
because the fluorescence yield decreases so rapidly at the same time 
that the two other influences are compensated (384). 

Furthermore, it is questionable whether the value of V, which is 
derived from the coefficient of diffusion and which determines the 
velocity of translation of the solvated molecules, can really be used in 
Equation (81a), or whether the dissolved molecule retains the pos- 
sibility of rotating within the sphere of the surrounding solvent 
molecules. At any rate, according to all published measurements, the 
degree of polarization decreases more rapidly than corresponds to a 
linear relationship between \\p and l/i? in the range of small viscosities 
of mixed solvents — for instance, in glycerol-water mixtures of high 
water content — while the decrease of Q r should produce an effect 
in the opposite direction. For uranin dissolved in very pure glycerol, 
p is found to be 45 % at room temperature ; if the same dye is dissolved 
in commercial glycerol containing a few per cent of water, p does not 
exceed 25 % at 20° C, and even at — 50° it is only 32 %, although the 
macroscopic viscosity of the solution is much larger then than the 
viscosity of pure glycerol at + 20° C (466).* 

Trypaflavine is easily dissolved in various alcohols but is only 
slightly soluble in ether. If this dye is dissolved in mixtures of an 
alcohol and ether, one obtains for each alcohol with increasing ether 
content a set of ^-values satisfying Equation (81a), but each of the 
straight lines representing 1/P as a function of Ij-q has a different slope 
and crosses the zero axis at a different height, although p is supposed 
to be determined by the ordinate of the crossing-point and to be a 
molecular constant (1303) (Figure 127). 

The very large discrepancy between the maximum polarization of 
the fluorescence of anthracene as measured by Perrin and listed in 
Table 68, and the values published by Chakravarti and Ganguli, 
must be mentioned in this connection. Perrin 's values were, obtained 
by the investigation of solutions in solid Canada balsam or in ethanol 
at — 180° C; the Indian scientists found that for the fluorescence of 
anthracene dissolved in water-free glycerol at — 79° C, p was 44 %, 
and they found similar values for the fluorescence of phenanthrene, 
naphthacene, chrysene, and perylene. The discrepancy greatly exceeds 

* The discrepancy cannot be explained merely by a partial depolarization 
of the fluorescence in the solution at low temperature because of beginning 
crystallization; on the other hand, all data on the polarization of fluorescence 
from solid solutions, which are never free from small inhomogeneities, are in 
general, too low and have only a qualitative significance (673). 



POLARIZATION OF FLUORESCENCE IN LIQUID SOLUTIONS 375 

all possible errors and must be due to some influence of the solvent. If 
the high values of p are correct, the lifetime of the excited state of 
anthracene would be even larger than calculated by Perrin (Table 68) 
(2 14b, 122 1). 

The phenomena which are observed in colloidal solutions prove 
that the rotational mobility of dye molecules in a solution is not 
determined by the macroscopic viscosity alone. The fluorescence of 
uranin or rhodamine in an ether-collodion solution is as little polarized 
as if the dyes were dissolved in pure ether, although the macroscopic 
viscosity is more than a thousand times greater. The comparison of 
solutions in ordinary gelatin and in so-called j8-gelatin is especially 
instructive in this respect. At a content of 91 % water, ordinary 
gelatin forms a thick jelly, while the viscosity of /J-gelatin is not more 
than 0.03. The polarization of the fluorescence of the the dyes dissolved 
in either of them, however, is the same. The important property is 
apparently not the viscosity of the solution, but the mobility of the 
molecules to which the dye is attached or on which it is adsorbed. 
In the ether-collodion solution, the dye remains dissolved in ether; 
in the gelatin-water solutions, it is adsorbed on the heavy gelatin 
molecules with their correspondingly small Brownian rotation. On the 
other hand, the polarizationof fluorescence never attains the maximum 
value which is observed in pure glycerol even in very stiff gelatin- 
water solutions, because when absorbed on gelatin the dye molecules 
retain a water envelope inside of which they still have a certain degree 
of rotational freedom (466, gio). 

These conditions are demonstrated most conclusively by the fluo- 
rescence of dyes which are adsorbed from a liquid solution on a gel 
of relatively large grains. If a sufficient amount of silica gel is immersed 
in an aqueous solution of trypaflavine, the solution is speedily dis- 
colored, and the fluorescence of the dye, which is almost completely 
adsorbed on the gel, is polarized up to 30 %, if the depolarization due 
to multiple reflection on the surfaces of the grains is eliminated by 
adequate means. If the same experiment is repeated with a solution 
in methanol, practically no adsorption takes place, the dye remaining 
in the liquid phase and the fluorescence being unpolarized. Intermediate 
instances are provided by other solvents like ethanol or amyl alcohol. 
If the gel with the adsorbed dye is removed from the water solution 
and carefully dehydrated, the degree of polarizationof the fluorescence 
is increased still further. This seems to prove that the dye molecules 
were not completely fixed on the gel surface as long as they were sur- 
rounded by an equally adsorbed envelope of water molecules (1301). 



376 



CONDENSED SYSTEMS 



Even if the relation between the polarization of fluorescence and 
the viscosity of the fluorescent solution which results from Equation 
(81a) can be verified only under especially favorable conditions, the 
general ideas leading to the equation are certainly sound. This is 
shown, for instance, by the fact that the degree of polarization becomes 
relatively high, even in solutions of small viscosity, if the lifetime of 
the excited state is very short. The exceedingly strong polarization of 
the fluorescence of erythrosin in aqueous solution, listed in Table 67, 
is a striking example of this kind. Even if the dye is dissolved in 
methanol, the polarization is still very appreciable, while it is zero in 
an acetone solution where the fluorescence yield becomes much larger. 
Rose bengale behaves similarly. 

If, in an aqueous solution of uranin, the high fluorescence yield 
and, simultaneously, the lifetime of the excited state are decreased by 
addition of a quencher, the polarization of the fluorescence is increased 
correspondingly and tends towards the limiting value p , as shown in 
Table 69. For uranin dissolved in glycerol and quenched by the addition 
of potassium iodide, Mitra found a degree of polarization equal to 
50 %, which is again higher than Perrin's p value* {1045,1046,1221). 
The polarization of the fluorescence of cyanoplatinites in iso- 
amyl alcohol also increases from 4.5 % to 10.5 % if the fluorescence is 
quenched to one-quarter of the maximum yield by the addition of 
aniline (775). 

Table 69 

Polarization p of the Fluorescence of Uranin Dissolved in Water 

in the Presence of KI 



Concentration 

of KI mole/liter . 





0.31 


1.09 


1.55 


3.72 


6.2 


Qr 


100 


18 


5 




1.2 


0.6 


P 


1.7 


6.2 


18 


24 


35 


40 



On the other hand, the fluorescence of uranyl salts in liquid 
solutions is always nonpolarized because of the relatively long lifetimes 
of the excited state (t = 10~ 6 to 10 — 4 sec), notwithstanding the fact 

* Discrepancies of this kind occur rather frequently in publications dealing 
with the polarization of the fluorescence of solutions. They are apparently due, 
in part, to the fact that many authors overrate the accuracy of their measure- 
ments. Another possible reason is the influence of the wavelength of the exciting 
light, an effect which has not been known for a long time and which has been 
neglected even in recent measurements. 



POLARIZATION OF FLUORESCENCE IN LIQUID SOLUTIONS 377 

that the molecules are anisotropic, as is proved by their behavior in 
the crystalline state. Discrepancies between earlier statements con- 
cerning the polarization of the fluorescence of canary glass were 
cleared up by Sevchenko. He found not only that various glasses 
behave differently but also that the degree of polarization of the fluo- 
rescence of an individual sample can vary within wide limits with 
varying wavelengths of the exciting light. Similar phenomena ob- 
served with many dye solutions will be discussed in the following 
section. The degree of polarization^) drops for all glasses to a minimum 
corresponding, in general, only to a few per cent when the fluorescence 
is excited by light of wavelengths 3650 and 2500A, as is the case in 
numerous experiments ; p reaches its highest values for exciting light 
of 4200 and 3200A. A maximum value of p = 25 % was obtained with 
a borosilicate glass; p was appreciably lower, not exceeding 13 %, for 
silicate glasses, and remained, regardless of the wavelength of the 
exciting light, constantly at the low level of 6 % for a phosphate glass 
(469,1224,1498). 

Furthermore, p decreases during the decay of the "slow fluo- 
rescence" and drops to about one-half of its initial value in about 10 _s 
sec after the end of the excitation. This effect is in conformity with 
Vavilov's theory mentioned in Section 113, but has never been ob- 
served directly in the fast-decaying fluorescence of dye solutions. 
Since the lifetime of the uranyl glass fluorescence is also of the order 
of magnitude of lO" 3 sec, an appreciable part of the fluorescence during 
the excitation period is due to an earlier absorption process and the 
values of p measured during a continuous irradiation are lower than 
they are if the phenomenon is observed under excitation by inter- 
mittent light flashes — for instance, in a phosphoroscope with both 
shutters opening and closing simultaneously (1498,1710 ,1762c). 

If a compound which is excited in aqueous solution by plane- 
polarized light (electric vector parallel to Z) emits unpolarized fluo- 
rescence, and if this fluorescence becomes partially polarized with 
its electric vector parallel to Z after the addition of a quencher, this 
can be explained only by the assumption that the components of the 
oscillation perpendicular to Z are more strongly quenched than the 
component parallel to Z. This is due to the fact that the angle y 
between the excited oscillator and the Z-axis increases with time be- 
cause of the Brownian rotation. Therefore, the observed quenching 
effect must be larger if the fluorescence is viewed in the direction of 
the Z-axis (with the electric vector perpendicular to Z) than if it is 
viewed in a direction perpendicular to Z This effect was observed by 



378 



CONDENSED SYSTEMS 



Sveshnikov * For the same reason, the r-values obtained by means of 
a Kerr-cell fluorometer, in which the exciting and the fluorescent light 
are always plane polarized, differ slightly for parallel or crossed po- 
larization of the two light beams, as has already been mentioned in 
Section 8 {66g,6y6,yji,i6ooa,i62^)_ 

As far as dye solutions are concerned, Equation (81a) holds only 
for solutions of very low concentrations (below 10~ 5 molar). At higher 
concentrations the interaction between molecules of the same kind has 
a depolarizing effect, which is due only to a small extent to the exci- 
tation of secondary fluorescence and which is practically independent 
of the viscosity of the medium: liquid and solid solutions behave 
alike (Table 70; Figure 128) (466). However, this "self -depolarizing" 
effect is also reduced if the lifetime of the excited state is decreased. 
If the fluorescence of the solution with the highest concentration in 
Table 70 (c = 2.5-10~ 2 ) is strongly quenched by the addition of 
aniline, the degree of polarization is raised from 6.25 to 30 % (218,383a, 
383c, 384,909). 



Table 70 

Polarization of the Fluorescence of Uranin in Glycerol, Excited 

by Plane-Polarized Blue Light as a Function of 

the Dye Concentration c 

(p' = observed polarization; p, the same, corrected for depolarization 

caused by secondary fluorescence) 



c 


2.5- 10-' 


2,5- 10-e 


2.5- 10- 6 


6-10- 8 


2.5- IO- 4 


1.15- 10- 3 


2.5-10- 3 J6-10~ 3 


1.25- 10-* 


p' 


40 


39.7 


33.6 


30.9 


28.9 


21.2 


17.1 


9.8 


6.25 


p 


40 


39.7 


39.4 


38.8 


36.2 


26.5 


21.4 


12.25 


6.25 



Self-depolarization is due to the fact that the molecules to which 
the excitation energy is transferred by resonance have a statistical 
distribution of orientation. The problem has been treated completely 
by Vavilov, including the probability of repeated transfers during the 
lifetime of the excited state (Section 113). It is, of course, not possible 
to apply Equation (81a) to this type of depolarization and thus to 
come to the conclusion that r increases with increasing concentration 

* In order to obtain the average quenching effect, the fluorescence should 
be viewed, according to Sveshnikov's calculations, in the direction of the Y-axis 
through a polarizer transmitting light with its electric vector at an angle 
a = 55° from Z(tan a = f^)- I* the exciting light is unpolarized, a should be 
33°. The direction of the exciting beam is again supposed to be parallel to the 
A* -axis. 



NEGATIVELY POLARIZED FLUORESCENCE OF ISOTROPIC SOLUTIONS 379 



of the fluorescent molecules {224). Self-depolarization becomes appre- 
ciable at concentrations about a hundred times lower than does self- 
quenching (Figure 116). At higer concentration, self -quenching fre- 
quently becomes very strong, and due to the corresponding decrease 
in t this sometimes even causes a renewed increase in the polarization 
of the fluorescence. Such a reversal has been observed, for instance, 
in solutions of rhodamine 
and trypaflavine in gly- 
cerol (1498,1761(1,17620). 

Some compounds, such 
as esculin, quinine sulfate, 
and sodium naphthionate 
show neither self-quen- 
ching nor self-depolari- 
zation. In canary glass 
both effects are also relati- 



40 



»* 



o. 20 



< 

— o— ■ 



10 



Concentration in I0" 3 g/cc (I0"V« *3-2 mole/liter) 



, Pig 128. Depolarization of fluorescence of 

vely small with increasing fluorescein sodium in glycerol as a function 
uranium concentration. of the dye concentration (Chauchois). 
This proves once more the 
parallelism of the two phenomena. 

120. Negatively Polarized Fluorescence of Isotropic Solutions. All 
statements made in the last section are correct only under the assump- 
tion that the processes by which the exciting absorption and the fluo- 
rescence emission are produced correspond to the same electronic 
transition. For dye solutions the excitation must take place by ab- 
sorption of light in the long-wavelength absorption band, which is 
only slightly displaced with respect to the fluorescence band, according 
to Stokes' law. If the wavelength of the exciting light is varied by 
shifting it beyond the peak of this band towards the ultraviolet, the 
polarization of the fluorescence decreases at first, passes through zero, 
and then even becomes negative. Finally, when the exciting light 
coincides with the next strong absorption band in the ultraviolet part 
of the spectrum, the polarization of the fluorescence again attains its 
initial positive value. This phenomenon was discovered by Froehlich 
and later corroborated by Levshin, Vavilov, and others for solutions 
of uranin, succinic fluorescein, eosin, rhodamine B, magdala red, and 
esculin (442,528,662,664,668,910,1756). 

The peak value p of the degree of polarization for all these 
compounds is close to 50 % ; the corresponding electronic transitions 
must be ascribed to oscillators which are very nearly linear and have 
identical orientation for the absorption and the emission processes. 



380 CONDENSED SYSTEMS 

Since, on the other hand, negative polarization can occur only if the 
absorbing oscillators form an angle larger than 54° with the emission 
oscillators, one must conclude that in the spectral region where the 
molecular absorption has a minimum the weak absorption that still 
prevails is not exclusively due to the tails of the strong absorption 
bands at greater and smaller wavelengths, but that it is caused, at 
least partially, by other electronic transitions corresponding to dif- 
ferently oriented oscillators. G. N. Lewis designates the strong ab- 
sorption bands producing fluorescence with positive polarization as 
*-bands and the weak absorption bands associated with negatively 
polarized fluorescence as ^-bands. Because of their weakness and be- 
cause they are overlapped by the tails of the *-bands, the y-bands 
frequently do not appear as peaks in the absorption spectra; the over- 
lapping also explains the continuous transition from positive to 
negative polarization and the relatively low degrees of negative po- 
larization which are usually observed (924). 

However, the absorption curve of fluorescein (Figure 129a) shows 
two secondary bands in the region of greatest negative polarization 
(1179) ; in the absorption and polarization curves of rhodamine (Figure 
1296), three weak absorption peaks at 4200, 3500, and 300A are almost 
exactly matched by maxima of negative polarization, while in the 
intervening regions the tails of the #-bands induce again a decrease in 
negative polarization (383a). Another example of this kind is provided 
by a solution of malachite green in a mixture of pentane, ether, and 
ethanol at — 158° C. The intense x- and *'-bands of this dye are 
situated at 6410 and 3175A, with a weakjy-band at 4310A. When the 
fluorescence is excited by the radiation from a sodium lamp or by the 
lines at 3130A of a mercury arc, the polarization is positive; under 
excitation with blue light the negative polarization attains a degree of 
— 17%, and in the case of a dye in which the nonsubstituted benzene 
ring of malachite green is replaced by an a-naphthyl group and which 
has a similar absorption spectrum, the negative polarization even 
reaches — 20 %, the highest degree of negative polarization which has 
been observed under these conditions (924). 

It is noteworthy that the strong positive polarization exhibited 
when the wavelength of the exciting light corresponds to the a; '-band 
drops again to zero at the short-wavelength edge of this band (Figure 
129), thus indicating that the mechanism of absorption changes once 
more in the far u.v. The suggestion that the #'-band itself, with a 
frequency which, in general, is close to double that of the #-band, is the 
first harmonic of the #-band, does not seem to be acceptable from the 



NEGATIVELY POLARIZED FLUORESCENCE OF ISOTROPIC SOLUTIONS 381 

viewpoint of the quantum-theoretical interpretation of electronic 
spectra. The persistent strong positive polarization in the region of 
great wavelengths corresponding to anti-Stokes excitation of the 
fluorescence proves that no appreciable part of this excitation is due 
to light absorption in another band of the y-type (compare Section 
103). 

The behavior of chlorophyll, with its narrow absorption and 
fluorescence bands, differs quantitatively from that of other dyes in 



50 

40 

sS 30 

E 20 
"a. 
10 



40 
30 
20 
10 



2000 3000 4000 5000 2000 3000 4000 5000 6000 A 

a b 

Fig. 129. Polarization of fluorescence as a function of the wave- 
length of the exciting light (Feofilov, Orndorff). 
a : fluorescein 1 : degree of polarization 

b : rhodamine 2 : absorption spectrum 

B extra in glycerol 3: fluorescence band 





















- 


,/- 






- 




f 










A 


/ 










.1 






. ^ 


J 






\ 














4 


r 












x' 

* 

/ r 




z 


\\ 


x' 

- i 






/ 1' 

2/ 1/ 


3 


i 1 > — . 


1 


i 


i 




i^ 


/ 1 \ 
/ \ 

1 


«■ 1 



that no negatively polarized fluorescence is observed. The first ab- 
sorption band of chlorophyll (R, at 6600A) coincides very nearly with 
the first fluorescence band, a second narrow absorption band ( V) is 
found at 4300A, and a third broader band (U) has its peak in the u.v. 
at 3800A. Every one of these bands corresponds to a different 
electronic transition and each produces a different degree of polari- 
zation in the red fluorescence (Table 71). If ris derived from measure- 
ments of p in solutions of variable viscosity according to Equation 
(81a), the same value (listed in Table 68) is arrived at regardless of 
the wavelength of the exciting light. Apparently, t is determined only 
by the lifetime of the excited state from which the emission takes 



382 



CONDENSED SYSTEMS 



place, while the lifetimes of the intermediate states, which are reached 
by the electronic transitions V and U, are much shorter. The last row 
of Table 71 gives the values of the angles a between the three ab- 
sorption and the emission oscillators, calculated according to the 
observed degrees of polarization (12 21). 

Table 71 

Maximum Polarization p g of the Red 

Fluorescence of Chlorophyll under 

Excitation by Light Absorbed in 

Different Bands 



Absorption 
band 


R 


V 


V 


A> •• 


43.5 


11 


23 


a . . . 


0° 


48° 


36° 



The indirectly excited slow fluorescence which is emitted by 
almost all solid dye solutions, especially at low temperatures, is, in 
most instances, not, or only very slightly, polarized, notwithstanding 
the fact that the normal fluorescence, which is observed under the 
same conditions, shows a strong positive polarization. The slow fluo- 
rescence of some dyes even exhibits a very pronounced negative 
polarization when they are dissolved in glycerol at — 180° C (Table 72) 
(1300). 

Table 72 
Polarization of the Slow Fluorescence of Organic Compounds 



Compound 


Trypaflavine* 


Rhoduline 
orange* 


Acridine 
orange* 


Eosin* 


E sculinf 


p of normal 

fluorescence . 
p of slow 

fluorescence . 


+•34 

— 13(— 9f) 


— 7.5 


— 5 


+ 44 



-f 32 




* Dissolved in glycerol, 
f Dissolved in gelatin. 



Slow fluorescence corresponds to a forbidden electronic transition 
from a quasi-stable state M to the ground state. On the other hand, 
the normal fluorescence is negatively polarized if it is excited by light 
which is very slightly absorbed in the ground state of the molecules ; 



POLARIZED FLUORESCENCE OF PARTIALLY ORIENTED MOLECULES 383 

and, finally, the strong absorption bands characteristic of the mole- 
cules in the quasi-stable state have the same polarization as the long- 
wave and ultraviolet absorption bands of the unexcited molecules (see 
Section 104). Hence, it seems that the strong absorption bands which 
correspond to allowed transitions have all oscillators oriented in the 
same direction in the molecule, while the oscillators corresponding to 
forbidden transitions, in general form, angles of more than 54° with 
respect to the others. 

The bands of slow fluorescence of dyestuffs in solid solutions, in 
general, overlap the normal fluorescence bands, and since they con- 
tribute some intensity to the total radiation emitted during the ex- 
citation period, the polarization of the fluorescence sometimes varies 
appreciably in different parts of the spectrum. Esculin in sugar, even 
at room temperature, shows green "slow fluorescence" of high in- 
tensity in addition to its normal blue fluorescence, and, therefore, the 
degree of polarization of the fluorescence, which is 39 % in the violet 
part of the fluorescence spectrum, drops to 25% in the green (i2g8). 

121. Polarized Fluorescence of Partially Oriented Molecules. 
Cellophane films are frequently characterized by a rather strong double 
refraction, the material being in itself optically anisotropic, with its 
optical £-axis parallel to the plane of the film. If a dye is absorbed on 
a cellophane film, the film acquires dichroism in the spectral region 
corresponding to the absorption bands of the dye (1025,1286,1505) ; 
if the fluorescence of the dye is viewed in the direction of the exciting 
radiation, it is partially polarized, even when excited by unpolarized 
light. A partial orientation of the dye molecules is caused by the 
directional forces of the absorbing material. Degrees of polarization 
as high as 12 % have been obtained under these conditions, the polari- 
zation being independent of the wavelength of the exciting light: 
for the oriented fraction of the dye molecules, p is not determined by 
the mode of excitation but only by the orientation and the nature 
of the molecules ; for the fraction which has no preferential orientation 
the polarization of the fluorescence is p = for any mode of excitation 
by unpolarized light. If the exciting light is plane polarized, the po- 
larization, which now depends greatly on the orientation of the optical 
axis £ of the film with respect to the electric vector of the exciting 
light z, can attain a much higher degree. Jablonski's measurements 
give not the real degree of polarization p, but the "apparent polari- 
zation" p z = [I Z — I X )I(I Z + I x ). This quantity drops to zero if the 
light is partially or even totally polarized with its electric vector form- 
ing an angle of 45° with the Z-axis. If & is the angle between the 



384 



CONDENSED SYSTEMS 



40 



20 



-20 



- 










- / 






°\ 




5^ 

\ 
\ 


/ 








" Vj 




\ 
\ 


t 








V 


/ 




i 


i 


, " 







-60 



-40 



20 



optical axis £ of the film and the electric vector of the exciting light, 
which is again supposed to be parallel to Z, the measured vaues of p z 
as a function of & are represented by curve a of Figure 1 30 and are in 
good agreenent with a theoretical equation derived by Jablonski. 
Curve b in the same figure is almost exactly symmetrical with curve a 
but has opposite si ns for p z ; it refers to the slow fluorescence of the 
same film at low temperatures (66i,6jo). 

A partial orientation of the dye molecules can also be obtained by 
dissolving them in so-called mesophases — for instance, in a concen- 
trated aqueous solution of am- 
monium oleate. The optical 
behavior of such a solution is of 
the same kind as that described 
above for cellophane films. The 
solutions are birefringent, they 
show dichroism, and their 
fluorescence is partially polar- 
ized. In most cases the vector 
of maximum fluorescence in- 
tensity coincides in its direction 
with the vector of strongest 
absorption. This is true for 
fluorescein and its derivatives, 
acridine dyes, etc.; only for a 
few dyes like primuline and 
some other azo dyes is the 
vector of maximum absorption 
perpendicular to the vector of 
strongest emission. The results 
obtained with chlorophyll are in perfect agreement with those 
obtained in isotropic solutions. The vector of the strongest fluores- 
cence emission is parallel to the vector of maximum absorption in 
the red band and forms an angle of more than 45° with the vector 
of maximum absorption in the violet band. Numerical data for 
these observations have not been published {1931). 

Finally, dye molecules, especially molecules consisting of long 
chains, can be oriented to a certain degree by imbedding them in a 
streaming solution. This is the method which was used by Scheibe in 
the investigation of the optical properties of the polymerized cyanine 
dyes. In a streaming solution the long chains formed by the poly- 
merization of the molecules are oriented parallel to the direction of the 



-20 

- e 





degrees 



Fig. 130. Polarization of the fluores- 
cence of euchrysine adsorbed on 
cellophane as a function of the 
angle 9 between Z and £ (Jablonski) . 
a: normaal fluorescence. fe:slow 
fluorescence at low temperature, 
both excited wit plane-polarized 
light. 



POLARIZED FLUORESCENCE OF CRYSTALS 



385 



flow (parallel to the Z-axis) and the solution shows the dichroism 
which is characteristic of the individual polymerized molecules. In the 
short- wavelength bands M x and M 2 (see Section 115), which appear 
in the solution even at low dye concentration, light is absorbed 
almost exclusively if its electric vector is perpendicular to the chain 
and parallel to the plane of the single molecules. Light is absorbed in 
the P-band when its electric vector is parallel to the chains (parallel 
to Z) (see Figure 131). Fluorescence which is caused by the same 
electric transition as absorption in the P-band also has the same orien- 
tation of the electric vector parallel to Z. The polarization of the fluo- 
rescence resulting from these mo- 
lecular properties is therefore 
positive if the exciting light is 
absorbed in the P-band and 
negative if the exciting light is 
absorbed in bands M x and M 2 . 
Fluorescence is strong if the 
electric vector of the exciting 
light is parallel to Z in the first 
case, or if it is perpendicular to 
Z in the second case. The degree 
of positive or negative polari- 
zation under these conditions 
sometimes reaches 70% and 
would probably be 100% if the 
chains were completely oriented 
parallel to Z. (If this extrapo- 
lation is correct, the fluorescence 
of the dye excited by plane- 
polarized light should show a polarization of 50 % even in a nonstream- 
ing solution with the chains oriented at random. Otherwise one would 
have to conclude that in a solution at rest the chains are no longer 
straight but curve irregularly in various directions). (g8ga,i4i4,i4i5) 

The relatively weak fluorescence which persists even when the 
electric vector of the exciting radiation is perpendicular to Z for light 
absorbed in the P-band or parallel to Z for light absorbed in the bands 
M x and M 2 , is due to those chains which are not fully oriented in the 
^-direction by the streaming solution. 

122. Polarized Fluorescence of Crystals. The spatial orientation of 
molecules, which is only partial in solutions under the conditions 
treated in the last section, becomes complete if the luminescent mole- 




6500 



6000 



5500 



5000 A 



Fig. 131. Absorption spectrum of 

pseudoisocyanine in polarized light 

(Scheibe). 

a: electric vector parallel to axis 

of polymerized molecules. 6 : electric 

vector perpendicular to axis of 

polymerized molecules. 



386 CONDENSED SYSTEMS 

cules are a part of a crystal lattice. The crystal lattice may consist 
exclusively of the luminescent molecules, as in uranyl or rare-earth 
salts, in pure anthracene, and in cyanoplatinites, or the luminescent 
molecules may be imbedded in a base lattice of another material, 
e.g., naphthacene in anthracene or chromium oxide in aluminum oxide. 
Even if the individual molecules are equivalent to linear os- 
cillators and if they are all oriented in a crystal, their fluorescence need 
not always be plane polarized. It is not necessary that all molecules 

\in the crystal be parallel to each 
\ VJ°i_V \ other; they may for instance, be 
■ '\ i\ | » j * subdivided into two groups which are 
\y |/ [/ '/ !/ tilted with respect to each other, 
/f ~ / /. A 7| forming an angle 0. This is indeed 

fl I the case in anthracene crystals, 

' Y \ where <P = 23° (Figure 132). In this 
,,.''* way, the fluorescence radiation is 
;!/ J/ / '/ partially depolarized; an angle <p = 

~A T ~f ~X 90° would even produce a complete 
1 ! | | j depolarization, 

i 1 J J I It is clear that the observed 

t~ ,™ ^ ■ *. ,■ i •, degree of polarization of the fluo- 
Fig. 132. Orientation of oscil- ° , , , . 

lators in anthracene crystals rescence depends on the orientation 
(Obreimow, Prikhotjko, and of the crystal with regard to the 
Shabaldas). direction of observation. With the 

exception of the cyanoplatinites, the 
degree of polarization of the fluorescence, is on the other hand, 
independent of the direction and the polarization of the exciting light, 
which influence only the probability of absorption and, thus, the 
intensity of fluorescence. For the "absorption oscillators" of the mole- 
cules are also anisotropic and oriented in the crystal, or, in other 
words, the crystals show dichroism in transmitted light. The direction 
of the electric vector which is most strongly absorbed prevails in all 
known cases also in the fluorescence light : absorption and emission 
oscillators are equally oriented in the lattice. 

Fluorescence of a microcrystalline powder in which the individual 
grains are oriented at random is always unpolarized when excited by 
unpolarized light. With plane-polarized exciting light, the conditions 
would be the same as in a solution of high viscosity if the polarization 
of the light were not destroyed by multiple reflection and refraction on 
the surfaces of the grains. This could be avoided only by imbedding 
the powder in a transparent liquid of identical refractive index. In 



POLARIZED FLUORESCENCE OF CRYSTALS 387 

general, observations must be made on single crystals, and, if only very 
minute samples are available, under the microscope. 

Anthracene crystals are monoclinic, those of naphthacene belong 
to another class of symmetry. Nevertheless, the green fluorescence of 
commercial anthracene, which is due to traces of naphthacene dis- 
solved in the anthracene, has, as far as its polarization is concerned, 
exactly the same properties as the blue -violet fluorescence of anthra- 
cene itself. In these small concentrations the impurity molecules are 
forced to take the same orientations as the molecules of the main 
substance. The crystals obtained by evaporation of a solution in 
hexane are thin flakes with surfaces parallel to the 001 plane; the 
optical "&-axis" lies in this surface, while the "«-axis" is perpendicular 
to it. If the fluorescence is observed in a direction perpendicular to the 
crystal face, the anthracene and naphthacene bands are partially 
polarized with their electric vector parallel to the 6-axis, or in the 
plane 010. Obreimow found p = 70% for the blue-violet bands, 
and from this value he derived the angle ifi = 23° mentioned above. 
Krishnan found p = 60 %* for the green fluorescence and also for 
the violet fluorescence of anthracene dissolved in phenanthrene. 
According to Krishnan, the electric vector component corresponding 
to the strongest absorption and emission is, in this case also, parallel to 
the 6-axis, which lies in the plane of the benzene rings, while the ab- 
sorption in smallest for the vector component parallel to the «-axis, 
which is perpendicular to this plane. The fluorescence radiation of 
dibenzanthracene crystals is partially polarized (j> = 33 %) with the 
electric vector parallel to the a-axis, and the same is true for the 
absorption (828,82ga,82gb,ii53). 

The dichroism of these crystals of aromatic hydrocarbons and 
the corresponding polarization of their fluorescence are caused by the 
different intensity of the oscillations in two directions perpendicular 
to each other, while the frequency of the absorption and emission 
bands is the same for both components within the accuracy of the 
observations. The absorption and fluorescence spectra of the uranyl 
salts, especially at low temperatures, are resolved into many line-like 
narrow bands which, in general/have different wavelengths for two 
orientations of the electric vector with regard to the crystal axes : the 
ordinary and extraordinary spectra do not coincide. At higher tem- 
peratures and in liquid solutions the bands overlap, and under these 
conditions a polarization of the resulting fluorescence radiation caused 
by the anisotropy of the molecules can be preserved only if the average 

* None of these values is reliable to within better than 10 %. 



388 CONDENSED SYSTEMS 

intensities of the lines in the ordinary and in the extraordinary spectra 
are different. No measurements concerning this question are available 
(79,634,1110, 1111,1117). 

Analogous results were obtained concerning the polarization of 
the fluorescence of europium salts.* Different groups of lines appear in 
the ordinary and extraordinary spectra of the hexagonal europium 
bromate crystal if the fluorescence is observed in a direction perpen- 
dicular to the optical axis c. If, however, the fluorescence is viewed in 
the direction parallel to this axis, only some line groups (e) of the 
ordinary spectrum are observed, and along with them several line 
groups (m) belonging to the extraordinary spectrum. This proves that 
of the lines observed under these conditions only the e-groups cor- 
respond to the emission by electric dipoles, while the w-lines originate 
from the oscillations of magnetic dipoles (280a). These conclusions 
are in perfect agreement with another observation which will be 
mentioned in the next section. In monoclinic or triclinic europium 
salts (sulfates or acetates), the phenomena are similar though some- 
what more complicated. Because of the higher asymmetry of the 
molecular fields, certain forbidden lines appear in the fluorescence 
spectrum which are completely unpolarized for every direction of 
observation. 

In the spectra of the uranyl and europium salts, the relative 
displacements of the narrow lines in the ordinary and the extra- 
ordinary spectra are so small that they can be ascertained only with 
the aid of a spectrometer. On the other hand many of the cyanopla- 
tinites, most of which crystallize in uniaxial systems, show a 
dichroism so strong that they appear differently colored according to 
the direction and the polarization of the transmitted light. In this case 
the oscillators oriented perpendicular to each other have not only 
different amplitudes but also widely different frequencies. Further- 
more, the color and the polarization of the fluorescence of these crystals 
is determined by the direction and polarization of the exciting light. If 
the latter is polarized with the electric vector perpendicular to the 
optical axis c of a barium cyanoplatinites crystal, the fluorescence is 
red and also polarized perpendicular to c (ordinary spectrum) ; if the 
exciting light is polarized parallel to c, the fluorescence is yellow and 
polarized parallel to c (extraordinary spectrum). Hence, the color of 
the fluorescence changes from red to orange and yellow if the fluo- 



* The polarization of the fluorescence of other rare-earth salts has not yet 
been investigated. 



ANGULAR INTENSITY DISTRIBUTION OF FLUORESCENT RADIATION 389 

rescence is excited by unpolarized light and if it is viewed in varying 
directions or through a Nicol at varying orientations (947b). 

According to Mani, the fluorescence of diamond is unpolarized 
when it is excited by unpolarized light and observed in a direction 
perpendicular to the primary light. The fluorescence is polarized with 
p = 80 % when the exciting light is plane polarized with its electric 
vector perpendicular to the direction of observation; the degree of 
polarization drops to 20 % if the electric vector of the exciting light is 
rotated by 90° so that it is parallel to the direction of observation. This 
result seems to be incompatible with any theoretical interpretation 
because unpolarized radiation can be decomposed into two components 
of plane-polarized light and, therefore, it should produce the same 
effect as the superposition of two such radiations (974). 

The polarization of the fluorescence of ruby and similar crystals 
will be treated in Section 167. 

123. Angular Intensity Distribution of the Fluorescent Radiation. 
Knowledge of the angular intensity distribution of the fluorescence 
emanating from a luminescent surface or a luminescent volume is 
important in the calculation of the fluorescent yield, which must be 
derived, in general, from the measurement of the fluorescence intensity 
emitted in a certain direction within a narrow solid angle Am. The 
problem is simple if the fluorescence is unpolarized and if the fluo- 
rescent medium is transparent to the fluorescence radiation and has 
perfectly smooth boundaries. In this case, the angular intensity 
distribution has spherical symmetry and the light intensity emitted 
by a given volume is the same for every direction. However, the light 
emanating from the plane surface of such a fluorescent medium does 
not obey Lambert's cosine law; instead, the apparent brightness of an 
element of the surface increases with increasing foreshortening of the 
surface (Lommel's law). If the fluorescence coming from a liquid 
solution or a polished glass is observed at increasing angles the ex- 
pected increase in apparent brightness is counteracted in part by the 
reflection at the boundary between liquid or glass and air, the re- 
flection becoming total at a certain angle. If this phenomenon is 
avoided by an adequate choice of the second medium, the observed 
brightness, which is represented in Figure 133 as a function of the 
angle of observation, is in excellent agreement with the values 
calculated from Lommel's law (947 'a, 948,1861). 

If the fluorescence is strongly reabsorbed by the fluorescent 
medium and re-emitted in all directions as secondary fluorescence, the 
angular intensity distribution is exactly the same as for the thermal 
Pringsheim 14 



390 



CONDENSED SYSTEMS 



80 



z 
uj 40 






radiation of an opaque surface : it follows Lambert's law. This is true, 
for instance, for the surface resonance radiation of sodium vapor (see 
Section 20). If, instead of being smooth and transparent, the surface is 
coarse — for instance, if it consists of a finely divided microcrystalline 
powder so that the fluorescence undergoes a great number of reflections 
and refractions — the angular intensity distribution of the fluorescence 
is closer to Lambert's than to Lommel's law (1426).* 

The conditions are less simple if the fluorescence is partially 

polarized, since, then, the angular 
intensity distribution no longer has 
spherical symmetry. If the fluores- 
cence of a dye in a viscous medium 
has a polarization of p % under 
excitation by plane-polarized light, 
and if the fluorescence is excited by 
unpolarized light, (100 — p)% of 
the fluorescence radiation has a 
spherical intensity distribution, while 
for the other p% the intensity is 
twice as strong in the direction of the 
primary light as in the direction 
perpendicular to the exciting beam. 
(With p — 50 %, a degree of polari- 
zation which is very nearly attained for many dyes in pure glycerol, 
the fluorescence intensity observed in the YZ-plane would be only 
83.3 % and the intensity observed in the X-direction 1 16.7 % of the 
average intensity). 

The total angular distribution depends on the intensity distri- 
bution of the radiation coming from each individual molecule with 
respect to the axis of this molecule and on the orientation of the 
different molecules with respect to each other. For most liquid so- 
lutions the spherically symmetrical intensity distribution corre- 
sponding to total depolarization of the fluorescence is caused by the 
random orientations of the individual molecules and by their Brownian 
rotation. Even under these conditions the angular distribution of the 
radiation from individual molecules can be determined by means of 
wide-angle interference experiments of the kind first performed by 
Seleny. The method was applied later by Freed, Weissman, and others. 
In these experiments the radiation which is emitted in two directions 
by an exceedingly thin film of a fluorescent solution is brought to 
* Also see Bibliography (/, Fig. 203). 



0° 10° 20" 30" 

ANGLE OF OBSERVATION 

Fig. 133. Fluorescence inten- 
sities of an aqueous dye solu- 
tion as a function of the angle 
of observation [Wood (1861)]. 



ANGULAR INTENSITY DISTRIBUTION OF FLUORESCENT RADIATION 391 

interference. From the interference patterns appearing when the 
angle of divergence between the two interfering beams is varied from 
30 to 90 degrees, the angular intensity distribution can be derived for 
the radiation from the individual radiating molecules, and this pro- 
vides a means of determining the nature of the oscillators from which 
the radiation originates. Thus, it could be shown that the normal 
fluorescence of fluorescein, as well as its slow fluorescence, is caused by 
the oscillations of electric dipoles. On the other hand, some of the lines 
in the fluorescence spectrum of europium were found to correspond to 
magnetic dipoles, in complete agreement with the conclusions drawn 
from the polarization of these lines which were mentioned in Section 
122 (308,435,1489-1492,1763,1817). 

Another method by which the nature of the emitting oscillators 
can be determined has been discussed by Vavilov. The fluorescence is 
observed in a direction perpendicular to the direction of the exciting 
light and the orientation of the electric vector of the latter is gradually 
changed. The law according to which the polarization of the fluo- 
rescence varies under these conditions, is different for radiations 
emanating from an electric dipole, a magnetic dipole, or an electric 
quadrupole. The method has not been applied directly. However, 
Sevschenko compared the behavior of a cube of canary glass with that 
of a fluorescein solution exhibiting the same maximum fluorescence 
polarization. From the fact that the curves representing p as a 
function of the orientation of the electric vector in the exciting light 
coincided, he concluded that the nature of the emitting oscillators was 
the same in both instances and, therefore, that the oscillators re- 
sponsible for the fluorescence of the uranyl ions were also electric 
dipoles. Feofilov showed also by this method that the carriers of 
fluorescence and phosphorescence in fluorescein were identical (383a, 
1498,1761a). 



CHAPTER V 

FLUORESCENCE OF ORGANIC COMPOUNDS 
A. The Luminescent Systems 

124. Chromophors and Fluorogens. Fluorescence was first dis- 
covered in aqueous solutions of a wood extract (lignum nephriticum) . 
Solutions of plant extracts and, later, of synthetic dyes were for a long 
time the most important objects of the investigations, which were 
naturally restricted to the visible region of the spectrum. It is plausible, 
therefore, that the first attempts to find relations between the fluo- 
rescence of a compound and its constitution were based on the semi- 
empirical but well-developed laws which had been established by the 
chemistry of dyestuffs. The strong absorption of visible light which is 
characteristic of dyes was ascribed to the presence of certain un- 
saturated groups, such as the azo group - N = N -, the ethylene group 
- HC = CH -, and the carbonyl group > C = O, which were called 
chromophors. These chromophors were at first supposed also to be the 
carriers of fluorescence as "luminophors." 

While the production of organic compounds with strong absorp- 
tion of visible light was, of course, the main purpose of the dye 
manufacturers, it is not important for the theoretical explanation of 
fluorescence whether the absorption and emission bands are located 
in the visible or the u.v. region. As already stated in the preceding 
chapters, certain radicals — for instance, the NH 2 -group — retain 
their characteristic absorption frequencies almost unaltered when they 
form a part of a larger molecule. The absorption bands of dyes, how- 
ever, and, as a matter of fact, of most aromatic and of many aliphatic 
compounds, cannot be ascribed to an individual chromophor group, 
but belong to the molecule as a whole. They are related to "quantum 
mechanical resonance phenomena" which occur when the molecules 
contain chains of conjugated double bonds. The most simple case of 
this type is the resonance between the two Kekule structures of ben- 
zene. The ion of trypaflavine may be mentioned as a more complicated 
example : its two principal resonating structures are 

392 



CHROMOPHORS AND FLUOROGENS 393 




H 2 N=f 



In general, the wavelength of the absorption band resulting from the 
resonance is the greater, the longer the chain of conjugated double 
bonds, and, simultaneously, the intensity of the absorption increases. 
Furthermore, an absorption band has a greater intensity, in general, 
if an electric charge has different locations in the resonating structures, 
so that the conversion of one structure into the other corresponds to 
the displacement of an electric charge as is the case in the trypaflavine 
ion. None of these rules, however, is rigidly exact* {4.08a, 408b, J509). 

It is beyond the scope of this book to deal more fully with the 
quantum-mechanical theory of color. Even if this theory were much 
more advanced than it actually is, it would not be able to determine 
the conditions under which an organic compound is fluorescent. Apart 
from the fact, which was already known to Stokes, that a substance 
must absorb the light by which it is excited to fluorescence, the ability 
of a compound to re-emit the absorbed energy in the form of lumi- 
nescence has very little to do with its capacity for light absorption. 
One cannot even say that substances with a very high absorption 
coefficient, corresponding to a short lifetime of the excited state, have 
a greater probability of being fluorescent because their chance of 
being quenched is smaller. For instance, benzene is fluorescent, 
although its absorption coefficient is low, while the majority of dye 
solutions with a thousand times stronger absorption coefficients are 
not fluorescent. 

This discrepancy had been recognized long before the introduc- 
tion of quantum theory. In order to explain it, the hypothesis had 
been proposed that in addition to its chromophor a fluorescent 
molecule must contain a "fluorogen." Most of these fluorogens were 
supposed to have a ring structure, the benzene ring being the most 
important of them. According to the theory developed in preceding 
chapters the absence of fluorescence in many compounds is caused by 
the fact that a competing process induces the deactivation of the 
excited molecule with greater probability than the radiating return to 
the ground state. If a compound is not fluorescent under any con- 

* For instance, the absorption coefficients of pentacene and rubrene are 
of the same order of magnitude as those of dyestuff ions, although the transitions 
between the principal resonance structures of these hydrocarbons are not con- 
nected with the displacement of an electric charge. 



394 FLUORESCENCE OF ORGANIC COMPOUNDS 

ditions, it must be assumed that this competing process is due not to 
the interaction with foreign molecules but to internal conversion. 
Internal conversion seems to be less frequent in molecules with the 
rigid structure which is greatly favored by the formation of closed 
rings. This is the modern version of the fluorogen hypothesis. Thus, 
nearly all known aromatic hydrocarbons which consist exclusively of 
condensed phenyl rings are fluorescent. Other very instructive 
examples will be pointed out in the section on synthetic dyes. The rule, 
however, is again not completely unequivocal; there are compounds 
consisting of long open chains of conjugated double bonds, such as the 
diphenylpolyenes and even purely aliphatic polyenes of the type 
CH 3 -(CH = CH)„-CH 3 , which are fluorescent in liquid solutions. 

If an organic compound is fluorescent, its emission band corre- 
sponds to the same electric transition as its absorption band of greatest 
wavelength (its "first absorption band"). In a few cases the two bands 
coincide ; more frequently, the center of the emission band is displaced 
by a relatively small distance toward greater wavelengths, in agree- 
ment with Stokes' law. Therefore, the rules evolved for the relation 
between constitution and color (wavelength of the absorption band) 
can be applied to the color of the fluorescence (but not to its existence). 
A substitution by which the absorption band of a compound is shifted 
in the direction of greater or shorter wavelengths will, in general, have 
the same influence, at least qualitatively, on the fluorescence band. 

The ability to emit fluorescence can be increased or reduced and 
even completely suppressed in a compound by certain substitutions. 
The majority of papers dealing with this matter does not distinguish 
sufficiently between a real decrease in fluorescence yield and a change 
in fluorescence intensity caused by a change in absorption power or a 
shift of the absorption and the fluorescence band to the ultraviolet, so 
that both are rendered "invisible." An extreme example of this 
kind occurs, if by hydration of the central carbon atom in a dye 
molecule the chain of double bonds is broken and the compound is 
transformed into the leuco base (for an example, see Table 80). In the 
latter, the first absorption band is shifted to the u.v. and may corre- 
spond, for instance, to the characteristic frequency of two benzene 
rings which are no longer conjugated; it is not improbable that such a 
molecule exhibits an ultraviolet fluorescence. If, on the other hand, the 
absorption coefficient of a fluorescent dye is enhanced by the intro- 
duction of so-called auxochrome groups, such as NH 2 , OH, or N(CH 3 ) 2 , 
a simultaneous increase in fluorescence intensity does not indicate a 
greater fluorescence yield. 



INFLUENCE OF ISOMERISM 395 

There are, however, certain substitutions in dye molecules which 
decrease their fluorescence yield greatly without an appreciable change 
of their absorbing power. These are, in the first place, the halides (in 
the order of increasing activity : CI, Br, and I) and the ions of iron and 
nickel. The influence of the introduction of halides as substituents for 
hydrogen atoms in the dyes of the fluorescein series has been mentioned 
in Section 106. And, while all porphyrins are fluorescent; even when 
two of their hydrogen atoms are substituted by metal ions, such as 
2Na+ or Mg++, the fluorescence is completely suppressed if the ions 
Co ++ ,Ni++, and Fe++ are introduced instead.* It is very striking that 
these substituents are the same elements which act as strong quenchers 
in liquid solutions — the halides, even in the same order of efficiency. 
It is probable that their ability to decrease the fluorescence yield, both 
as "quenchers" in liquid solutions and as substituents entering into 
the molecules themselves, is related to the relatively small energies 
which are sufficient to alter their electric charges (Fe++ *i Fe +++ or 
I5P±I - , etc.). By this property they are enabled to induce reversible 
chemical reactions with molecules of the solvent by which the exci- 
tation energy is dissipated. 

The hypothesis that the inhibition of fluorescence by the metals 
of the iron group is related to their magnetic properties, is without any 
rational base. 

125. Influence of Isomerism. The influence of isomerism on the 
wavelengths ftf the emission bands of doubly substituted benzene or 
naphthalene derivatives is not very large and is rather irregular, as 
shown by several examples in Tables 76 and 80. A rule stating that the 
fluorescence intensity is always strongest in the ortho compounds, 
weaker in the meta, and weakest in the para compounds was based 
on observations which did not take into account variations in the ab- 
sorption of the exciting light. Bowen measured the fluorescence yields 
of the three xylenes excited by the line 2537A and found them to 
be 29 % for o-, 30 % for m- and 41.5 % for ^-xylene, a result which is 
in direct contradiction to the older empirical rule (E,i4$). 

Isomers corresponding to cis- and foms-modifications of a 
compound show, in general, greater dissimilarities in their fluo- 
rescence. Cis- and towts-stilbene have been thoroughly investigated by 
G. N. Lewis. The absorption spectra of the two isomers differ widely: 
their first absorption bands are shown in Figure 134a. By light ab- 



* The phosphorescence of crystal phosphors is also quenched very ef- 
fectively by contamination with iron, nickel, and cobalt. 



396 



FLUORESCENCE OF ORGANIC COMPOUNDS 



sorption in these bands either of the two compounds is converted into 
the other with a quantum yield of approximately 30%. Also, cis- 
stilbene is transformed partially (10 % yield), into a nonidentified non- 
fluorescent compound. Cw-stilbene is not fluorescent and, thus, the 
remaining energy must be lost by internal conversion. A weak fluo- 
rescence which is obtained after long-lasting irradiation of cis-stilbene 

can be ascribed unequivocally to 
freshly formed <nms-stilbene. The 
latter modification emits a strong 
and very characteristic fluorescence 
in solutions as well as in the solid 
crystalline state (Figure 1346) (com- 
pare Section 136). The fraction of 
the excitation energy which is dis- 
sipated by trans-stilheae molecules 
in processes of internal conversion 
is not known. Therefore, no reliable 
conclusions concerning the fluores- 
cence yield can be derived from a 
knowledge of the photochemical 
efficiency. At any rate, the probability 
of internal conversion is much larger for the cis- than for the trans- 
modification. G. N. Lewis ascribes this to the fact that the molecule 
of toms-stilbene is planar, while in cis-stilbene the two phenyl rings 
cannot lie in the same plane (g2g). 




2600 A 



Fig. 134a. Molar extinction 

coefficient e of cis-(\) and 

trans-(2) stilbenes (Lewis, 

Magel, and Lipkin). 




4800 



4400 



4000 



3600 



3400 A 



Fig. 1346. Fluorescence spectrum of trans-stilbene 
(Lewis, Magel, and Lipkin) in ether-alcohol 
mixture at - 90°C. (l)andcrystallineat - 190° (2). 



Cis- and fraws-stilbamidine show the same characteristic behavior. 
The nonfluorescent «'s-modification is converted by irradiation into 
the irans-modification which exhibits a strong blue fluorescence, and 



INFLUENCE OF STATE OF AGGREGATION 397 

vice versa. Dimerization is supposed, in this case, to be a second 
process by which irradiation converts the ^raws-modification into 
another nonfluorescent compound (602a., 602b). 

Lewis mentions, incidentally, that the all-^raws-modification of 
lycopene is practically nonluminescent ; if the compound is subjected 
to a short heat treatment, some of the cj's-forms are produced, which 
exhibit normal fluorescence as well as slow fluorescence (compare 
Sections 136-138). According to Stobbe, one of two isomeric modifi- 
cations of octatetraene in the crystalline state is white and emits a 
blue fluorescence, while the other is yellow with a bright green fluo- 
rescence (927a, 1583). While 7-hydroxycoumarin (umbelliferone) is 
brilliantly fluorescent in alkaline solution under near u.v. excitation, 
its isomer with the hydroxy group in the 6-position shows no visible 
fluorescence {198). 

The problem of the influence of isomerism is of still a different 
kind if the fluorescent compounds consist of chains or fused ring 
systems containing conjugated double bonds. In this case the number 
of double bonds in an uninterrupted chain can vary in different 
isomers and, thus, their absorption and emission spectra and their 
faculty of fluorescing can be quite dissimilar. Numerous examples of 
this type will be found in subsequent sections. There are, however, 
many instances in which the influence of isomerism on the fluorescence 
spectrum of polycyclic compounds.cannot be explained by this or any 
other simple theoretical assumption. Thus, no change in the system of 
conjugated double bonds occurs in the various dimethylalloxazines ; 
nevertheless, the fluorescence of 6,7-, 6,8-, and 5,8-dimethylalloxazine 
is described by Karrer and Musante as sky-blue, bluish green, and 
greenish yellow, respectively (721). 

According to Schlenk and Bergmann, 9,10-diphenyl-9,10- 
dihydroanthracene and several of its derivatives exist in three isomeric 
modifications, of which only one shows a strong violet fluorescence in 
solution (compare Section 130) (1438). 

126. Influence of State of Aggregation. The greatest part of earlier 
investigations, as well as of more recent papers, is concerned with the 
fluorescence of organic compounds in liquid solutions. The solvents 
were most frequently water, alcohol, hexane or other aliphatic 
compounds; benzene, toluene, etc., are less advantageous because 
their absorption bands lie in the region of greater wavelengths and 
because they are themselves fluorescent. 

The fluorescence yield of pure liquid compounds, such as benzene 
and its derivatives, is very low, on account of self-quenching. The 
Pringsheim 14* 



398 FLUORESCENCE OF ORGANIC COMPOUNDS 

fluorescence of pure crystalline anthracene, which is still strong 
immediately below the melting point, vanishes completely as soon as 
the substance is liquified. The fluorescence spectra of compounds which 
are not ionized in solutions are, in general, the same for the vapors, 
solutions, and solid crystals, the bands being only slightly displaced in 
the direction of greater wavelengths, by passing from the vapor to the 
solution and to the crystal. This is true especially for colorless com- 
pounds with fluorescence bands in the u.v., the violet, or the blue. Most 
deeply colored substances which show a characteristic fluorescence in 
the vapor state or in dilute solutions are very little or not at all fluo- 
rescent as crystals. Examples are napthacene, and other polycyclic 
condensed hydrocarbons, in contrast to anthracene, phenanthrene, 
fluorocyclene, and naphthalene ; the dark-colored, almost copper-like 
crystals of the diphenylpolyenes with more than three ethylene groups 
also cannot be excited to fluorescence. Crystalline dyes, such as fluo- 
rescein, eosin, and the rhodamines, which have such high absorption 
coefficients in certain regions of the visible spectrum that the re- 
flection becomes metallic, are not fluorescent, even at the temperature 
of liquid nitrogen. A weak yellowish fluorescence is excited by near- 
u.v. light in the microcrystalline powder of trypaflavine, which is 
orange-yellow without the metallic luster characteristic of the dyes 
mentioned above ; and a light yellow dye, which has been prepared by 
G. Schwarz, exhibits a very brilliant yellow luminescence under black 
light illumination, while its fluorescence in alcoholic solution is blue- 
green and relatively weak* (1291,1721). Another example of this type 
is the fairly strong, dark-red fluorescence of isocyanine chloride, which 
is not luminescent in liquid solutions; the broad red emission band 
of the solid does not seem to be related to the narrow yellow band of 
the polymerized molecules which are formed in concentrated aqueous 
solutions. Still another group of compounds which are fluorescent in 
the solid state and not in liquid solutions is mentioned by H. Kauff- 
mann. Among them are aminobenzalmalononitrile [(CH 3 ) 2 N-C 6 H 4 - 
CH(CN) 2 ], dimethylamino-a-phenylcinnamonitrile [(CH 3 ) a N-C 6 H 4 - 
* The formula for this nameless dye is: 

kA N J- CH = CH-NH-Q 

Dyes of almost identical constitution in which, for instance, the oxygen of the 
oxazine ring is replaced by sulfur or selenium, and which have practically the 
same absorption spectrum, are not fluorescent in the solid state. 



INFLUENCE OF STATE OF AGGREGATION 399 

CH - C(CN)C 6 H 6 ], and ^-dimethylaminophenyl [(CH 3 ) 2 NC 6 H 4 - 
C(CN)C 6 H 6 ], with a strong orange, green, and bright red fluorescence, 
respectively. Other compounds of the same type, which are brilliantly 
luminescent in the solid state, can be excited to a much weaker fluo- 
rescence of a different color when they are dissolved in alcohol or 
pyrimidine. Since all these compounds contain the cyanogen group, 
Kauffmann assumes that this is the cause of their behavior, as it is 
supposed to be in the case of the cyancplatinites (compare Section 
149) {E, 734,735,737)- 

If no unequivocal relation exists between the fluorescence spec- 
trum of a crystalline compound and the spectrum of the vapor 
or of a dilute liquid solution, the possibility must be considered that 
the emission by the solid is not characteristic of the bulk material but 
of an impurity which may be present in very small quantities. Thus, 
the green fluorescence of all commercial anthracene is caused by an 
admixture of naphthacene, the blue fluorescence of phenanthrene is 
caused by anthracene which can be removed only by adsorption 
methods, the blue fluorescence of fluorene is probably due to anthracene 
and carbazole, etc. According to Winterstein, carbazol can be ex- 
tracted from many supposedly pure anthracene samples and shows, 
when highly purified itself by chromatographic methods, a bright blue 
fluorescence. Campbell succeeded however, in completely suppressing 
this fluorescence by even more careful purification (ig8,i858). The 
probability of contamination with some impurities exists, to a still 
higher degree, in more complex compounds, especially if they are not 
of a synthetic nature but are derived from some plant extracts. There- 
fore, most of the statements published on the fluorescence of solid 
alkaloids (morphine, papaverine, etc.), interesting as they would be if 
they were correct, cannot be accepted as being reliable (14,15). The 
only exceptions are quinine and its salts, which have been tested in 
carefully purified samples. 

At liquid-air temperature the diffuse band spectra of many 
crystalline organic compounds are resolved into groups of narrow 
sub-bands or lines. Under these conditions similarity with the spectra 
of the vapors becomes even more evident. The splitting of the broad 
bands has been observed in the spectra of benzene, the xylenes, 
naphthalene, etc., and also of more complex hydrocarbons, such as 
decacyclene and several others. In some instances (for example, 
naphthalene and the diphenylpolyenes), the fluorescence spectra of 
the crystals show at low temperature an even more pronounced 
structure than those of the vapors. 



400 



FLUORESCENCE OF ORGANIC COMPOUNDS 



127. Influence of Solvent. The relation between the nature of the 
solvent and the fluorescence yield of dissolved compounds has already 
been mentioned in Section 106. The influence of the solvent on the 
exact spectral location of the fluorescence bands has been a matter of 
discussion for a long period. It has been suggested that the color of the 
fluorescence shifts continuously from violet to red with increasing 
dielectric constant of the solvent ; the data in Table 73a have frequently 
been brought forward as proof for this hypothesis. Other examples 
can easily be found, however, which seem to prove exactly the 
contrary (Table 73b) (1406,1407a). The search for connections with 

Table 73 

Relation Between the Wavelength of the Fluorescence Bands 

and the Dielectric Constant ft of the Solvent 

a. Dimethylnaphtheurhodine 



Solvent 


Ligroin 


Ether 


Pyridine 


Acetone 


Levulinic 
acid 


Ethanol 


Methanol 


fl .... 

Color of fluo- 
rescence 


1.86 
green 


4.37 
green- 
yellow 


8.08 
yellow 


12.4 
orange- 
yellow 


20.7 
orange- 
yellow 


26.3 
orange 


31 
orange- 
red 



b. Anthracene 



Solvent 


Benzene 


Toluene 


Xylene 


Ether 


Amyl 
alcohol 


Ethanol 


Metha- 
nol 


Vapor 


A* 

Wavelengths . 
of main 
fluorescence 
bands . . 


2.25 
4060 
4285 

4570 


2.35 
4050 
4270 

4550 


2.57 
4050 
4260 

4535 


4.37 
4035 
4225 

4535 


16.7 
4030 
4250 

4500 


26.3 
4020 
4260 

4500 


31 
3998 
4220 

4480 


3900 
4150 

4320 



other properties of the solvent, such as its dipole moment, were no 
more successful. This seems to be due to the fact that the superimposed 
influences of polarity (molecular electric moment) and index of 
refraction (dielectric constant for high frequencies) can act either in 
the same or in opposite directions. According to results published by 
Sheppard, the absorption bands of a great many dyes are shifted quite 
regularly toward greater wavelengths with decreasing index of re- 
fraction of the solvents, as long as only solvents of the same polarity 
are taken into account. It is certainly justified to assume that this rule 
holds also for the fluorescence bands, although no actual measurements 
are at hand. It is another question whether the rule can be applied 
to other types of dissolved organic compounds. 



INFLUENCE OF SOLVENT 



401 



In a similar way the nature of the adsorbent acts on the fluo- 
rescence spectra of adsorbed dyes. This can be observed at its best if 
the fluorescence spectrum consists of relatively narrow bands, and has, 
for instance, been shown for hematoporphyrin adsorbed on various 
supports. An even better example is provided by the almost linelike 
narrow absorption and emission band of the polymerized isocyanine 
dyes, as shown in Table 74 {56,1414). 

Table 74 

Absorption and Fluorescence Bands 

of Adsorbed Isocyanine Chloride 



Adsorbent substance 


Absorption 
band in A 


Fluorescence 
band in A 


Glass 

Quartz (cryst.) . . 

Mica 


5728 
5767 
5720 
5793 


5727 
5806 



The problem is, of course, of a different kind if the nature of the 
dissolved molecules is altered by a reaction with the solvent. Such 



1 




I 3 














*»\ 












\\l \ 


/A 




1 


" i 



30000 

v in cm 



40000 
-1 



Fig. 135. Absorption spec- 
trum of naphthylamine 
(Ley and Graefe). 
1 : naphthylamine in al- 
cohol. 2 : naphthylamine 
with 10% HC1 in alco- 
hol. 3: naphthalene in 
alcohol. 

Pringsheim 14** 



5000 



/ 


s -^. 
























wv> 


















V* 


>v * f"\ 


"•#'\'Vv\ 



20000 



30000 



2500A 
I 

2 
3 
4 



40000 



-1 



Fig. 136. Fluorescence spectrum of 

naphthylamine in alcohol (Ley and 

Graefe) . 

1: pure naphthylamine. 1 2— 4: 

increasing addition of HC1. 

5: naphthalene and benzene 

for comparison. 



402 



FLUORESCENCE OF ORGANIC COMPOUNDS 



reactions can consist either of a change in the state of ionization (see 
Section 116) or in the formation of a new compound. If, for instance, 
hydrochloric acid is added in increasing concentration to solutions of 
aniline or naphthylamine, the absorption and fluorescence bands of 
these compounds give way to bands similar to those of benzene or 
naphthalene, respectively (Figures 135 and 136). The amino groups 
are successively replaced by NH 3 Cl-groups and these substituents 
influence the characteristic frequencies of the nonsubtituted hydro- 
carbons to a much smaller degree than the amino groups [937). 

B. Aromatic Hydrocarbons and Heterocyclic Compounds 



128. Benzene. J. Stark discovered the fluorescence of benzene in 
liquid solutions long before the fluorescence of the vapor had been 
observed. The solvents were alcohol, water, hexane, carbon tetra- 



,...'■ illlllUit...lJllllii, iilililn 



iL_iii^i 



I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I II I I I I I I I I I M II I 1 I I 



ll 'I i. 



Au-IL. 



2600 



2700 



2800 



2900 3000 A 



Fig. 137. Schematic representation of fluorescence 
spectrum of benzene (Kronenberger and Pringsheim). 



a : vapor at high pres- 
sure 
b: solid at - 180° C 
c: solid at 0° C 



d: liquid at 0° C 
e-g:m°/ , 10%, and 

4% solutions in 

ethanol 



chloride, and ether. The emission spectrum is analogous to that of the 
vapor insofar as it consists of a progression of bands with a spacing 
A v = 1000 cm -1 adjoining a similar progression of absorption bands 
which are separated by intervals A v = 920 cm -1 . The structure of the 
bands is, however, almost completely blurred out, the only trace of it 



FLUORESCENCE OF BENZENE 



403 



consisting in a secondary maximum at the long-wavelength side of 
each band (303,1350,1546). The distance by which the bands are 
displaced with respect to those of the vapor depends not only on the 
nature of the solvent, but even to a greater degree on the con- 
centration of the solution. In very dilute alcoholic solutions the centers 
of the bands coincide almost exactly with those in the vapor spectrum 
and the wavelength shift becomes noticeable only at higher concen- 
trations. The values in the third and fourth rows of Table 75 are, 
therefore, exact only for a well-defined concentration. This is shown 
schematically in the last three rows of Figure 137. 

Table 75 

Absorption and Fluorescence Bands of Benzene 

(Wavelengths of the short-wavelength edges in A) 





6 



5 



4 



3 




2 




1 









1 



2 



3 



4 



5 





V* 


6 








Vapor ■< 


'Abs. 
Fl. 


2275 


2324 


2363 


2416 


2471 


2528 
2541 


2589 
2602 


2667 
2667 


2739 


2815 


2895 


2980 


30 


Alcohol 
solution 


f Abs. 
[Fl. 


2290 ? 


2330 


2378 


2428 


2485 


2547 


2598 
2599 


2681 
2679 


2754 


2827 


2910 


3005 ? 




Pure at 
25 c C* 


fAbs. 
1.F1. 


2297 


2339 


2385 


2432 


2488 


2550 


2608 


2689 
2686 


2761 


837 


2920 







In pure liquid benzene the emission bands are very diffuse and so 
weak that only the strongest bands can be observed. The melting point 
of benzene is at + 5° C, but the liquid can be undercooled to below 0°. 
If the undercooled liquid is made to crystallize, the fluorescence bands 
recover the full intensity and relative sharpness corresponding to the 
optimum concentration in a dilute solution (compare Section 112) and 
a short afterglow can be observed phosphoroscopically. The fine 
structure of the bands appears, however, only if the crystals are cooled 
to a temperature below — 100° C. 

Just as the fluorescence of the vapor at high pressures, the fluo- 
rescence of crystalline benzene at — 180° C is independent of the 
wavelength of the primary light. The emission spectrum is the same 
whether the fluorescence is excited by the u.v. continuum of a hy- 
drogen lamp, by the total radiation of a mercury lamp, or by the 
monochromatic line 2537A. Whereas the absorption bands are still 
further resolved at the temperature of boiling hydrogen, no better 
resolution of the fluorescence spectrum can be obtained at — 259° than 
at — 180° {835,1556). Although the analogy between the spectra 



404 FLUORESCENCE OF ORGANIC COMPOUNDS 

represented in the first two rows of Figure 137 is obvious, a correlation 
of the individual bands of the crystal spectrum with those of the vapor 
spectrum has not met with much success. From an analysis of the 
crystal absorption spectrum its O'-O" band could be identified with a 
weak band at 37,829 cm' 1 (2641A), which thus is displaced by 261 
cm -1 with respect to the O'-O" band of the vapor (Figure 138). The 
strongest band series with a spacing of 990 cm -1 starts in the fluo- 
rescence spectrum of the crystals at a distance of 600 cm -1 from the 
O'-O" band and corresponds to the progression designated as B in the 



3130 2536.7 




1III 



Fig. 138. Fluorescence spectra of benzene excited by 
Hg-arc (Kronenberger and Pringsheim) . This figure was 
made from the original prints, but spectrum d has been 
enlarged so that its dispersion matches the others, as 
indicated by the arrows. 
a : Hg comparison c : solid benzene at 0° C 

spectrum d: solid benzene at 

b: fluorescence of ben- — 180° C 

zene vapor at 20° C 

vapor spectrum (Section 88). Only one other series originating at a 
distance of 970 cm -1 from the O'-O" band has been identified by 
Sponer with some certainty as corresponding to one of the weaker 
progressions of the vapor spectrum. Several of the smaller frequency 
interval recurring in the crystal spectrum have been ascribed ten- 
tatively to lattice vibrations {835,836,1545). 

129. Derivatives of Benzene. Fluorescence spectra of monocyclic 
benzene derivatives in liquid solutions are collected in Table 76. Most 
of these spectra are closely related to that of benzene itself, as is the 
case in the spectra of the vapors. However, they are again more 
diffuse and shifted in the direction of greater wavelengths. These 
effects are especially pronounced if an H-atom of the phenyl ring is 
replaced by a hydroxyl or an amino group, while the introduction 
of methyl groups has relatively little effect. A comparison of the spectra 
of biphenyl and diphenylmethane shows that the interaction 



CONDENSED AROMATIC HYDROCARBONS 405 

between the phenyl rings becomes appreciably weaker if they are 
separated by a CH 2 -group. On the other hand, the fluorescence 
spectrum of biphenyl, which is always described as diffuse and weak 
in the vapor, shows some structure and is fairly strong in solutions. 
According to Bowen, the fluorescence yield of biphenyl dissolved in 
hexane is 22%, about twice as large as that of benzene listed in 
Table 61. This difference in the behavior of the vapor and the solution 
may be explained by the stabilizing effect mentioned in Section 83h. 
In all spectra the maxima are superimposed on a strong continuous 
background. Although frequency differences occur between individual 
maxima which are of the same order of magnitude as those in the 
benzene spectrum, the maxima never form series with a constant 
spacing and are probably due to the superposition of a number of 
progressions. A theoretical analysis of these spectra is, therefore, not 
possible, and this is further emphasized by the fact that the data 
published by various authors differ widely in many details. Most of the 
figures of Table 76 are taken from a recent paper by Ley and Specker in 
which the wavelengths of the band are stated without any attempt to 
arrange them in regular series (934338,1689). 

The spectra observed at low temperatures in the crystalline 
modifications show, again, more structure than those of undercooled 
glasses. Both types of emission spectra, however, are only more or less 
modified forms of the spectra characteristic of the vapors or the liquid 
solutions. Luminescence spectra of an essentially different type can 
occur if thin films of benzene derivatives are condensed on a metal 
surface at the temperature of liquid air. They are shifted far into the 
region of greater wavelengths and seem no longer to be related to the 
first absorption bands. Thus, a band between 5125 and 6410A 
(maximum at 56 15 A) has been observed by Terenin in the lumi- 
nescence spectrum of bibenzyl under these conditions, while the normal 
fluorescence bands of this compound lie near 3000A (Table 76). 
Similar new emission bands are obtained when aromatic compounds 
are dissolved in solids or adsorbed on gels at low temperatures. Ap- 
parently the conditions for the appearance of these luminescence 
bands, which are always combined with an appreciable afterglow, 
were also provided by Terenin's experimental arrangement (compare 
Section 136) (1640). 

130. Condensed Aromatic Hydrocarbons. The absorption and 
fluorescence bands of the hydrocarbons in which a series of benzene 
rings are fused in a straight chain have increasing wavelengths with 
increase in number of rings and of conjugated double bonds (numbers 



406 



FLUORESCENCE OF ORGANIC COMPOUNDS 



Table 76 

Fluorescence Spectra of Benzene Derivatives in Liquid Solution 

in Alcohol (A) or Hexane (H) 

(Band limits and band maxima in A) 



(A) Benzene . . 

C 6 H 6 
(A) Toluene . . 

C 6 H 6 CH 3 

(A) Xylene . . , 
C 6 H 4 (CH 3 ) 2 



(A) Mesitylene . . . 

C 6 H 3 (CH 3 ) 3 
(H)Durol 

C 6 H 2 (CH 3 ) 4 
(A) Phenol* 

C 6 H 6 OH 

(A)Cresol J° 

C 6 H 4 (OH) 2 \™ 

(A) Hydroxybenzoic f o 

acid \m 

HOC 6 H 4 COOH \_p 
(A) Aniline 

C 6 H 5 NH 2 
(A) Anisidine . . ..Jo 

CH 3 OC 6 H 4 NH 2 \p 
(A) Tolunitrile . . ..jo 

CH 3 C 6 H 4 CN \ p 
(H) Biphenyl 

C«H B C,H B 
(H) Diphenylmethane 

C 6 H 6 CH 2 C 6 H 5 
(H) Bibenzyl 

C 6 H 5 CH 2 CH 2 C 6 H 5 
(H) Dibenzylethylene . 

C 6 H 5 CH 2 CH : 
CHCxi 2 C 6 Hg 
(H) Diphenyl ether* . . 

C 6 H 5 OC 6 H 5 
(H) Diphenylamine . . 

(C 6 H 6 ) 2 NH 



2550-3000 
2599 2635 2639 2754 2827 2910 

2610-3000 
2622 2646 2676 2740 2809 2886 

2600-3200 
2603 2636 2680 2713 2798 2896 3038 3135 

2670-2820 

2685 2715 2802 

2650-2900 

2681 2739 2801 2865 

2650-3000 

2698 2712 2747 2786 2863 2972 

2800-3400 

continuous 

2870-3500 

continuous 

2870-3850 

2860-3850 )■ continuous 

2920-3850 

3760-4800 

3280-4440 )> continuous 

3230-4080 

3000-4100 
continuous with weak maxima 3048 3355 

3130-4290 . 

3390-4230 > continuous 

2870-3760 

2800-3510 

2940-3650 
2940 3048 3140 3190 3270 3406 3550 

2720-3200 
2750 2790 2845 2935 3015 

2700-3200 
2750 2790 2835 2910 3040 

2700-3200 

2785 2835 2960 3060 3140 
2840-3680 

continuous 
3260-4150 
continuous 



continuous 



* The analogous compounds in which O is replaced by S are not fluorescent. 



FLUORESCENCE OF CONDENSED AROMATIC HYDROCARBONS 407 

1-5 in Table 78). The fluorescence spectra of crystalline naphthalene, 
anthracene, and phenanthrene at the temperature of boiling hydrogen 
were analyzed by Obreimow and Prikhotjko. They identified some of 
the principal frequency differences occurring in each of these spectra 
with infrared and Raman frequencies of the hydrocarbons. However, 
the coincidence is not quite convincing in several cases. Moreover, 
numerous nuclear frequencies not known from any other investigations 
had to be introduced for the complete representation of more than 100 
lines measured in the naphthalene spectrum, some of which had a 
width of only 0.2A (5 cm -1 ), and the overall appearance of the spectra 
did not show the clear periodicity characteristic of the low temperature 
fluorescence spectrum of crystalline benzene. Considering the uncer- 
tainty of the interpretation of even this spectrum, Obreimow's 
analysis of the much more complicated spectra cannot be accepted 
without some reserve (1153,1154,1266). 

The manifold luminescence spectra which are excited in naphtha- 
lene under various experimental conditions are collected as a typical 
example in Table 77. The processes by which some of these spectra 
are produced will be discussed in later sections. 

The fluorescence yield increases from benzene through naphtha- 
lene to anthracene and drops rapidly for the aromatic hydrocarbons 
containing more than three phenyl rings in a straight chain. This holds 
for liquid solutions as well as for pure solids. The fluorescence of 
pentacene dissolved in benzene is very weak, and it is below the limit 
of observability in the crystals. (Compare Table 53). When naphtha- 
cene is dissolved in anthracene or in other hydrocarbons, such as 
1 ,2-benzanthracene and 1, 2, 5, 6-dibenzanthracene, however, its lu- 
minescence becomes exceedingly strong. An admixture of 10"*% 
naphthacene, which is present in all anthracene not especially purified, 
suffices to make the green naphthacene bands appear brighter in the 
fluorescence spectrum than the violet bands of anthracene, while at 
the concentration of 0.1 % the latter are completely suppressed. At 
a naphthacene concentration exceeding 0.1 %, the intensity of the 
green fluorescence decreases again, apparently due to self-quenching. 
If the green and the violet bands are observed simultaneousl